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

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7.How many solutions for 2cos(x/2) + 1 = 0 on the interval?a) oneb) twoc) threed) fourd) 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 sinx+ cosx= 0 isx= 0.
10. An equivalent trigonometric expression forcos(Ο€+x)is
11.Which of the following properly expresses𝑐??120Β°with a compound angle formula?a)?𝑖?90𝑐??30+ ?𝑖?30𝑐??90c)?𝑖?90𝑐??30βˆ’ ?𝑖?30𝑐??90b)𝑐??90𝑐??30+ ?𝑖?30?𝑖?90d)𝑐??90𝑐??30βˆ’ ?𝑖?30?𝑖?90
312. Which expression is a proper simplification of2?𝑖?2???(?)
3
[A 6 marks]Question 13-15 requires brief solution. 2 marks for each question.13. Solvesin(2?)=√2on the interval3?πœ‹
14. Solve?π‘Ž?2?+ ?π‘Ž??= 0on the interval?
15.Solve2cos(0.5x)=βˆ’βˆš3on the interval?a)? =πœ‹3b) ? =πœ‹3,7πœ‹3c) ? =5πœ‹3d)? =5πœ‹12,7πœ‹12,17πœ‹12,19πœ‹12
44[C 4 marks] 16. Using the formulas studied this unit, determine the exact value of the following.Show allsteps.a)sin5πœ‹12b)sec (105Β°)[C3 marks]17. Simplify:sin (2βˆ’ ?) + sin(πœ‹ βˆ’ ?) + cos (3πœ‹2βˆ’ ?) βˆ’ sin(2πœ‹ βˆ’ ?)[T 6 marks] 16. Givencosπœƒ =4, where3πœ‹2≀ πœƒ ≀ 2πœ‹andsin𝛼 =1213whereπœ‹2≀ 𝛼 ≀ πœ‹, determine the exactvalue ofa)cos(2πœƒ)b)sin(𝛼 + πœƒ)πœ‹1.
55[A 6 marks] 18. Solve the equations below on domain[0, 2πœ‹]a)2 cos2? = 7 cos ? βˆ’ 6b)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 thediagram below.Determine the height of the satellite above the surfaceof the planet to the nearest kilometer.
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