Question 1: Evaluate each of the following:

Answer:

i)

ii)

iii)

iv)

v)

vi)

vii)

viii)

Question 2: Find the value of \theta in each of the following:

Answer:

i)

ii)

iii)

Question 3: Evaluate / Prove the following:

Answer:

i)

ii)

iii)

iv)

v)

vi)

vii)

vii)

viii)

ix)

Question 4: Express each of the following in terms of trigonometric ratios of angles between and .

Answer:

i)

ii)

Question 5: Prove that:

i)

ii)

Answer:

i) LHS

Hence Proved.

ii) LHS

RHS.

Hence Proved.

Question 6: If , prove that:

Answer:

Given

LHS

RHS

Hence Proved.

Question 7: If and are interior angles of triangle ABC, prove that

Answer:

Given

Question 8: Find if when is an acute angle.

Answer:

Given

Question 9: If , when and are acute angles, find the value of .

Answer:

Given

Question 10: If and are interior angles of , show that

i) ii)

Answer:

i) Given

ii) Similarly,

Question 11: Find the value of for

i) where

ii) where

Answer:

i)

ii)

Question 12: Prove the following:

i)

ii)

iii)

Answer:

i) LHS

RHS

Hence Proved.

ii) LHS

RHS

Hence Proved.

iii) LHS

Question 13: What is the max value of i) and ii)

Answer:

i)

ii)

Question 14: If , find the value of

Answer:

Question 15: If , what is the value of

Answer: