 # 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(π+x)is
11.Which of the following properly expresses𝑐??120°with a compound angle formula?a)?𝑖?90𝑐??30+ ?𝑖?30𝑐??90c)?𝑖?90𝑐??30− ?𝑖?30𝑐??90b)𝑐??90𝑐??30+ ?𝑖?30?𝑖?90d)𝑐??90𝑐??30− ?𝑖?30?𝑖?90
312. Which expression is a proper simplification of2?𝑖?2???(?)
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[A 6 marks]Question 13-15 requires brief solution. 2 marks for each question.13. Solvesin(2?)=2on the interval3?𝜋
14. Solve?𝑎?2?+ ?𝑎??= 0on the interval?
15.Solve2cos(0.5x)=−√3on the interval?a)? =𝜋3b) ? =𝜋3,7𝜋3c) ? =5𝜋3d)? =5𝜋12,7𝜋12,17𝜋12,19𝜋12
44[C 4 marks] 16. Using the formulas studied this unit, determine the exact value of the following.Show allsteps.a)sin5𝜋12b)sec (105°)[C3 marks]17. Simplify:sin (2− ?) + sin(𝜋 − ?) + cos (3𝜋2− ?) − sin(2𝜋 − ?)[T 6 marks] 16. Givencos𝜃 =4, where3𝜋2≤ 𝜃 ≤ 2𝜋andsin𝛼 =1213where𝜋2≤ 𝛼 ≤ 𝜋, determine the exactvalue ofa)cos(2𝜃)b)sin(𝛼 + 𝜃)𝜋1.
55[A 6 marks] 18. Solve the equations below on domain[0, 2𝜋]a)2 cos2? = 7 cos ? − 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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