Further Trigonometry (DP IB Maths: AA HL)

Solve the following equations in the given intervals. 

(i)

(ii)

Show that .

Hence find the exact value of when  for .

Show that .

Hence solve the equation  for the interval . Show each step of your working.

Show that  can be written in the form , where  and .

Give  in the form where  is an integer.

Given that  and  , find the exact value of .

Prove that .

Solve the equation for the interval .

Prove the identity .

Solve the equation   for  .

Determine the value of the following expression

The following diagram shows the triangle  where , and .

Find the length giving your answer in the form , where .

Find the value of .

Solve  algebraically for .

By writing  in the form  where and , or otherwise, solve .

Let where  

Express in terms of .

Given that  for and  for  , find the value of . Give the answer in the form  where , and  are prime numbers.

By writing and finding a similar expression for , or otherwise, show that

Hence show that .

Prove that .

By writing  and finding a similar expression for , or otherwise, show that

Hence solve  for  .

The following diagram shows the triangle where ,  and

Expand and simplify .

Show that the length of  is units.