Relationship Between Trigonometric Ratios (DP IB Analysis & Approaches (AA)): Revision Note

Relationship Between Trigonometric Ratios

What is the relationship between sine and cosine?

• and

• You can see this using a right-angled triangle with hypotenuse of length 1

  • The two other angles can be labelled and

  • The sides can be found using trigonometry

How do I find the exact value of a trig ratio given a different one?

• If you know the exact value of one trig ratio

  • then you can find the exact values of the other ratios

• One method involves drawing a right-angled triangle and using SOHCAHTOA

  • For example, given that

    • Label the hypotenuse

    • Label the opposite side

    • Find the adjacent side using Pythagoras' theorem

    • Find and using SOHCAHTOA

    • Check whether the value should be positive or negative

• Another method involves using trigonometric identities

  • For example, given that

    • Use to find

    • Use to find

    • Check whether the value should be positive or negative

How do I determine whether a trigonometric ratio will be positive or negative?

• You can determine whether a trigonometric ratio is positive or negative by looking at the size of the angle

  • You can use the unit circle or the graphs