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Trigonometry 00769700 answers
1. [pic]
Sin is –ve in 3rd and 4th quadrants; hence, x will be in these quadrants.
Hence, we will have x = 2400, 3000 or 4pi/3 , 5pi/3.
In general, we can write x = [pic] where n =0,1,2,…
2. [pic]
Or, cos2x(1-3sinx) = 0.
If cos2x = 0, we will have 2x = pi/2, 3pi/2
Or, x = pi/4, 3pi/4 = 0.79, 2.37 radians.
If 1-3sinx = 0, we will have x = sin-1(1/3) = 19.470,160.530 or 0.34,2.80 radians.
3. [pic]
If tanx = 0.618, x = tan-10.618 = 31.720, 217.720 or 0.55, 3.80 radians.
If tanx = -1.618, x = tan-1-1.618 = -58.280, 121.720 or -1.02, 2.12 radians.
4. [pic]
[pic]
[pic] Proved.
5. [pic] Proved.
6. [pic]
7. [pic]
[pic]
8. [pic]
[pic]
9. [pic]
Hence, it is an identity.
10. [pic]
11. [pic]
12. [pic]
13. [pic]
14. [pic]
[pic]
[pic]
[pic]
15. Plot of y = sin(-2x) is given below.
[pic]
16. [pic]
[pic]
Or, [pic]
Or, [pic]
Or, (3tanθ-2)(2tanθ+3)=0
Or, tanθ = 2/3, -3/2
We will have to consider +ve value as 0≤2θ≤pi, that is in 1st quadrant.
Hence, tanθ = 2/3, sinθ = 2/√13, cosθ=3√13
17. [pic], as α is in 1st quadrant.
[pic]
18. [pic], as angle is in 2nd quadrant.
[pic]
[pic] , as angle is in 4th quadrant.
Hence, [pic]
19. 2sinxcosx+sinx=0
Or, sinx(2cosx+1)=0
Hence, sinx = 0 or x = 0, pi, 2pi
If 2cosx+1 = 0 or cosx = -1/2 giving x = 2pi/3, 4pi/3
20. 2sin37sin26 = cos11-cos63 as 2sinAsinB = cos(A-B)-cos(A+B)
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