Answers
Answer:
70.9,109.1,204.0,336.0
Step-by-step explanation:
The solution set for the equation 6sin² θ - 7 sinθ - 5 = 0 in the interval [0,360)is {θ∈ [0,360)∣θ = 230.48 ,309.521}
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given equation is 6sin² θ - 7 sinθ = 5
Lets arrange in an order
6sin² θ - 7 sinθ - 5 = 0
a=6, b=-7 and c = -5
sinθ = 7±√49+120/12
Simplifying under the square root:
sinθ =7±17/12
Taking the positive solution first
sinθ =24/12
sinθ =2 (Not valid)
Now let's try the negative solution:
sinθ =7-17/12
sinθ =-10/12
sinθ =-5/6
θ= sin⁻¹(-5/6)
θ= −50.48⁰ ,−129.52⁰
we need to restrict our solution to the given interval [0,360), so we add 360 degrees to the negative angle:
θ=360−50.48 = 309.52 and 360 −129.52 =230.48
Therefore, the solution set for the equation 6sin² θ - 7 sinθ - 5 = 0 in the interval [0,360)is {θ∈ [0,360)∣θ = 230.48 ,309.521}
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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