7 how many solutions for 2cosx2 1 0 on the interval a

7. How many solutions for 2cos(x/2) + 1 = 0 on the interval ?
a) one b) two c) three d) four d) none of these
8. Given that tan(x) = 5/12, x lies in Q.1 , the exact value of sin(x) is 9. A solution to the trigonometric equation sin x + cos x = 0 is x = 0. 10. An equivalent trigonometric expression for cos(π+x) is
11. Which of the following properly expresses 𝑐??120° with a compound angle formula?
a) ?𝑖?90𝑐??30 + ?𝑖?30𝑐??90 c) ?𝑖?90𝑐??30 − ?𝑖?30𝑐??90
b) 𝑐??90𝑐??30 + ?𝑖?30?𝑖?90 d) 𝑐??90𝑐??30 − ?𝑖?30?𝑖?90

3
12. Which expression is a proper simplification of 2?𝑖?
2
?
? ?
(? )
3
[A 6 marks] Question 13-15 requires brief solution. 2 marks for each question.
13. Solve sin
(
2?) =
√
2
on the interval
3
?
𝜋
14. Solve ?𝑎?
2
? + ?𝑎?? = 0 on the interval ?
15. Solve 2cos(0.5 x)=−
√3
on the interval ?
a) ? =
𝜋
3
b) ? =
𝜋
3
,
7𝜋
3
c) ? =
5𝜋
3
d) ? =
5𝜋
12
,
7𝜋
12
,
17𝜋
12
,
19𝜋
12

4
4
[C 4 marks] 16. Using the formulas studied this unit, determine the exact value of the following. Show all
steps.
a) sin
5𝜋
12
b) sec (105°)
[C3 marks] 17. Simplify: sin (
2
− ?) + sin(𝜋 − ?) + cos (
3𝜋
2
− ?) − sin(2𝜋 − ?)
[T 6 marks] 16. Given cos𝜃 =
4
, where
3𝜋
2
≤ 𝜃 ≤ 2𝜋 and sin𝛼 =
12
13
where
𝜋
2
≤ 𝛼 ≤ 𝜋 , determine the exact
value of
a) cos(2𝜃) b) sin(𝛼 + 𝜃)
𝜋
1
.

5
5
[A 6 marks] 18. Solve the equations below on domain
[0, 2𝜋]
a)
2 cos
2
? = 7 cos ? − 6 b) cos2? + sin? = 0
[3 marks] 19. Prove the identity. Show at least 4 steps in working out.
sin(?+?)
sin ? cos ?
= 1 + tan ? cot ?
Bonus . A satellite is orbiting a small planet, as shown in the
diagram below.
Determine the height of the satellite above the surface
of the planet to the nearest kilometer.