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
Jim G.
Aug 7, 2017

#"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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