Question

Given the function value and quadrant restriction, find θ.
cosθ=.6561, interval (270°,360°)
θ ≈__°

Please explain step by step.

Answer 1

Answer on Question # 41414– Math - Trigonometry

Question:

Given the function value and quadrant restriction, find $\theta$.

$\cos \theta = .6561$, interval $(270{}^{\circ}, 360{}^{\circ})$

$\theta \approx \_$

Solution:

Trigonometric equation $\cos \theta = a$ has such general solution

$$\theta = \pm \arcsin a + 2\pi k, \quad k \in \mathbb{Z}.$$

For $a = 0.6561$, $\arcsin 0.6561 \approx 49{}^\circ$. As we need a solution from the interval $(270{}^{\circ}, 360{}^{\circ})$. Using general solution we can take $\theta = -\arcsin a + 2\pi = -49{}^\circ + 360{}^\circ = 311{}^\circ$.

Answer: $\theta \approx 311{}^\circ$.

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