What is the unit circle ?

The unit circle is a circle with radius 1 and centre (0, 0) , which can be used to calculate trigonometric values .

How are angles measured on the unit circle?

Angles on the unit circle are always measured from the positive x -axis . Positive angles are measured anti-clockwise and negative angles are measured clockwise .

True or False? Trigonometric functions have only one input for each output .

False. Trigonometric functions can have multiple inputs for each output .

What is a primary value in a trigonometric equation?

The primary value is the first solution given by a calculator for a trigonometric equation.

What is the first step in finding secondary values for a trigonometric equation using the unit circle ?

The first step in finding secondary values for a trigonometric equation using the unit circle , is to draw the angle into the first quadrant using the x or y coordinate to help you.

True or False? The unit circle can be used to calculate trigonometric values for angles greater than 90° .

True. The unit circle can be used to calculate trigonometric values for angles greater than 90° .

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IBMathsDPAnalysis & Approaches (AA)HLFlashcards3. Geometry & TrigonometryThe Unit Circle & Exact Values

The Unit Circle & Exact Values (DP IB Analysis & Approaches (AA))

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What is the unit circle?
The unit circle is a circle with radius 1 and centre (0, 0), which can be used to calculate trigonometric values.
How can the unit circle be used to find trig values?
Trig values can be found by creating a right-angled triangle between the x-axis and the radius of the unit circle.
How are angles measured on the unit circle?
Angles on the unit circle are always measured from the positive x-axis.
Positive angles are measured anti-clockwise and negative angles are measured clockwise.
What does the x-coordinate represent on the unit circle?
The x-coordinate on the unit circle gives the value of $\cos θ$ .
What does the y-coordinate represent on the unit circle?
The y-coordinate on the unit circle gives the value of $\sin θ$ .
How is $\tan θ$ represented on the unit circle?
On the unit circle, $\tan θ$ is represented by the gradient of the line from the origin to the point (x, y).
What is the CAST diagram?
The CAST diagram is a mnemonic for remembering which trigonometric functions are positive in each quadrant of the unit circle (Cosine, All, Sine, Tangent).
True or False?
Trigonometric functions have only one input for each output.
False.
Trigonometric functions can have multiple inputs for each output.
What is a primary value in a trigonometric equation?
The primary value is the first solution given by a calculator for a trigonometric equation.
What is the first step in finding secondary values for a trigonometric equation using the unit circle?
The first step in finding secondary values for a trigonometric equation using the unit circle, is to draw the angle into the first quadrant using the x or y coordinate to help you.
True or False?
The unit circle can be used to calculate trigonometric values for angles greater than 90°.
True.
The unit circle can be used to calculate trigonometric values for angles greater than 90°.
What is the exact value of the cosine of 0º?
The exact value of the cosine of 0º is 1.
$\cos (0) = 1$ .
What is the exact value of the sine of 90º?
The exact value of the sine of 90º is 1.
$\sin (90) = 1$ .
Remember, $90 º = \frac{π}{2} rad$ , so $\sin \frac{π}{2} = 1$ .
What is the exact value of the tangent of 0º?
The exact value of the tangent of 0º is 0.
$\tan (0) = 0$ .
What is the exact value of the tangent of $\frac{π}{4} rad$ ?
The exact value of the tangent of $\frac{π}{4} rad$ is 1.
$\tan (\frac{π}{4}) = 1$ .
Remember, $\frac{π}{4} rad = 45 º$ , so $\tan (45) = 1$ .
What is the exact value of both the cosine and the sine of 45º?
The exact value of both the cosine and the sine of 45º is $\frac{\sqrt{2}}{2}$ .
This can also be written as $\frac{1}{\sqrt{2}}$ .
$\cos (45) = \sin (45) = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$ .
Remember, $45 º = \frac{π}{4} rad$ , so $\cos (\frac{π}{4}) = \sin (\frac{π}{4}) = \frac{\sqrt{2}}{2}$ .
The sine of which angle (between 0º and 90º) has an exact value of $\frac{1}{2}$ ?
The sine of 30º has an exact value of $\frac{1}{2}$ .
$\sin (30) = \frac{1}{2}$ .
Remember, $\frac{π}{6} rad = 30 º$ , so $\sin (\frac{π}{6}) = \frac{1}{2}$ .
What is the exact value of the cosine of $\frac{π}{2} rad$ ?
The exact value of the cosine of $\frac{π}{2} rad$ is 0.
$\cos (\frac{π}{2}) = 0$ .
Remember, $\frac{π}{2} rad = 90 º$ , so $\cos (90) = 0$ .
The tangent of which angle (between 0 and $\frac{π}{2}$ ) has an exact value of $\frac{\sqrt{3}}{3}$ ?
The tangent of $\frac{π}{6}$ has an exact value of $\frac{\sqrt{3}}{3}$ .
$\tan (\frac{π}{6}) = \frac{\sqrt{3}}{3}$ .
Remember, $\frac{π}{6} rad = 30 º$ , so $\tan (30) = \frac{\sqrt{3}}{3}$ .
What is the exact value of the tangent of 60º?
The exact value of the tangent of 60º is $\sqrt{3}$ .
$\tan (60) = \sqrt{3}$ .
Remember, $60 º = \frac{π}{3} rad$ , so $\tan (\frac{π}{3}) = \sqrt{3}$ .
What is the exact value of the cosine of $\frac{π}{3} rad$ ?
The exact value of the cosine of $\frac{π}{3} rad$ is $\frac{1}{2}$ .
$\cos (\frac{π}{3}) = \frac{1}{2}$ .
Remember, $\frac{π}{3} rad = 60 º$ , so $\cos (60) = \frac{1}{2}$ .
What is the exact value of the sine of 0 rad?
The exact value of the sine of 0 rad is 0.
$\sin (0) = 0$ .
For which angle (between 0º and 90º) is the tangent of that angle undefined?
The tangent of the angle 90º is undefined.
Remember, $90 º = \frac{π}{2} rad$ , so the tangent of $\frac{π}{2}$ is undefined.
What is the exact value of both the cosine of $\frac{π}{6} rad$ and the sine of $\frac{π}{3} rad$ ?
The exact value of both the cosine of $\frac{π}{6} rad$ and the sine of $\frac{π}{3} rad$ is $\frac{\sqrt{3}}{2}$ .
$\cos (\frac{π}{6}) = \sin (\frac{π}{3}) = \frac{\sqrt{3}}{2}$
Remember, $\frac{π}{6} rad = 30 º, \frac{π}{3} rad = 60 º$ , so $\cos (30) = \sin (60) = \frac{\sqrt{3}}{2}$ .
What triangle can you sketch to help you remember the exact trig values for the angles of 30º $(\frac{π}{6} rad)$ and 60º $(\frac{π}{3} rad)$ ?
An equilateral triangle with edges of length 2, cut in half, can help you remember exact trig values for 30º $(\frac{π}{6} rad)$ and 60º $(\frac{π}{3} rad)$ .
What triangle can you sketch to help you remember the exact trig values for an angle of 45º $(\frac{π}{4} rad)$ ?
An isosceles right triangle with two edges of length 1, can help you remember the exact trig values for 45º $(\frac{π}{4} rad)$ .

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The Unit Circle & Exact Values (DP IB Analysis & Approaches (AA))

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Cards in this collection (26)

1. Number & Algebra

Number & Algebra Toolkit

Exponentials & Logs

Sequences & Series

Simple Proof & Reasoning

Proof by Induction & Contradiction

Binomial Theorem

Permutations & Combinations

Complex Numbers

Further Complex Numbers

Systems of Linear Equations

2. Functions

Linear Functions & Graphs

Quadratic Functions & Graphs

Functions Toolkit

Other Functions & Graphs

Reciprocal & Rational Functions

Transformations of Graphs

Polynomial Functions

Inequalities

Modulus Functions & Further Transformations

3. Geometry & Trigonometry

Geometry Toolkit

Geometry of 3D Shapes

Trigonometry

The Unit Circle & Exact Values

Trigonometric Functions & Graphs

Trigonometric Equations & Identities

Inverse & Reciprocal Trigonometric Functions

Trigonometric Proof & Equation Strategies

Vector Properties

Vector Equations of Lines

Vector Planes

4. Statistics & Probability

Statistics Toolkit

Correlation & Regression

Probability

Discrete Random Variables

Binomial Distribution

Normal Distribution

Continuous Random Variables

5. Calculus

Differentiation

Techniques & Applications of Differentiation

Integration

Techniques & Applications of Integration

Optimisation

Kinematics

Basic Limits & Continuity

Further Differentiation

Further Integration

Differential Equations

Maclaurin Series

Limits using l'Hôpital's Rule & Maclaurin Series