Finding the expression of a reflex angle?

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Finding the expression of a reflex angle?

The reflex angle $theta$ is such that $costheta = k$ , where $0 < k < 1$ .
(i) Find an expression, in term of k, for
(a) $sintheta$ ,
(b) $tantheta$ .
(ii) Explain why $sin2theta$ is negative for $0 < k < 1$ .

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Answer 1 · 2017-08-07T17:46:23

$"see explanation"$

Explanation:

$theta>180^@" and costheta>0$

$"which places "theta" in the fourth quadrant"$

$•color(white)(x)sintheta=+-sqrt(1-cos^2theta)$

$sintheta" however, is negative in the fourth quadrant"$

$rArrsintheta=-sqrt(1-k^2)$

$tantheta=sintheta/costheta=(-sqrt(1-k^2))/k$

$sin2theta=2sinthetacostheta=-2ksqrt(1-k^2)$

$sqrt(1-k^2)>0to-sqrt(1-k^2)<0$

$rArrsin2theta<0$

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Finding the expression of a reflex angle?

The reflex angle $theta$ is such that $costheta = k$ , where $0 < k < 1$ .
(i) Find an expression, in term of k, for
(a) $sintheta$ ,
(b) $tantheta$ .
(ii) Explain why $sin2theta$ is negative for $0 < k < 1$ .

1 Answer

Explanation:

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Finding the expression of a reflex angle?

The reflex angle thetatheta is such that costheta = kcostheta = k, where 0 < k < 10 < k < 1. (i) Find an expression, in term of k, for (a) sinthetasintheta, (b)tanthetatantheta. (ii) Explain why sin2thetasin2theta is negative for 0 < k < 10 < k < 1.

1 Answer

Explanation:

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The reflex angle $theta$ is such that $costheta = k$ , where $0 < k < 1$ .
(i) Find an expression, in term of k, for
(a) $sintheta$ ,
(b) $tantheta$ .
(ii) Explain why $sin2theta$ is negative for $0 < k < 1$ .