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# C2 Trig Identities Questions watch

1. I don't know why I keep getting these wrong, answers at the bottom, thanks

1) 3sin²θ + sinθ = 0
(answer is 0, 180, 199, 341, 360)

2) tan²θ - 2tanθ - 10 = 0
(answer is 77.0, 113, 257, 293)

3) sin²θ - 2sinθ - 1 = 0
(answer 204,336)

4) tan²2θ = 3
(answer 30,60,120,150,210,240,300,330)

5) 4sinθ = tan θ

(answer 0, 75.5, 180, 284, 360)

thanks
2. 5) 4sinθ = tanθ
4sinθ = sinθ/cosθ
4sinθcosθ - sinθ = 0
sinθ(4cosθ-1) = 0

sinθ = 0 or cosθ = 1/4

θ = 0, 180, 360 or θ = 75.5 , 284.5
3. you have an excess amount of brain, let me cream some off you, einstein

cheers
4. 4) tan²2θ = 3
tan2θ = ±√3

2θ = 60, 240 , 420 , 600 or 2θ = -60 , 120 , 300 , 480 , 660

So, θ = 30 , 60 , 120 , 150 , 210 , 240 , 300 , 330
5. (Original post by mockel)
5) 4sinθ = tanθ
4sinθ = sinθ/cosθ
4sinθcosθ - sinθ = 0
sinθ(4cosθ-1) = 0

sinθ = 0 or cosθ = 1/4

θ = 0, 180, 360 or θ = 75.5 , 284.5
i dont get the -sinθ bit, where did that come from?

edit: nevermind, got it now.
6. 3) sin²θ - 2sinθ - 1 = 0

Using the quadratic formula:

sinθ = [2 ± √(4+4)] / 2

sinθ = (2 ± 2√2)/2

sinθ = 1±√2

sinθ cannot be greater than 1, hence

sinθ = 1-√2

θ = -24.5 , 204.5 , 335.5

Therefore, θ = 204.5 , 335.5
7. 2) tan²θ - 2tanθ - 10 = 0

Using the quadratic formula:

tanθ = [2 ± √(4+40)] / 2

tanθ = (2 ± 2√11)/2

tanθ = 1±√11

θ = 77.0 , 257.0 or tanθ = -66.7 , 113.3 , 293.3

So, θ = 77.0 , 113.3 , 257.0 , 293.3
8. 1) 3sin²θ + sinθ = 0
sinθ(3sinθ+1) = 0

sinθ = 0 or sinθ = -1/3

θ = 0 , 180 , 360 or θ = -19.5 , 199.5 , 340.5

So, θ = 0 , 180 , 199.5 , 340.5 , 360
9. could you be any smarter

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