Question

sin theta = 0.5, then cos theta.tan theta. sec theta.csc thera.cot theta=​

Answer 1

Answer:

If sine theta is 0.5 or 1/2,

cosine theta is √3/2

tangent theta is 1/√3

cosecant theta is 2

secant theta is 2/√3

cotangent theta is √3

This can easily be determined by either the formulae of trigonometry or a right triangle diagram. I'll explain with the latter.

We know that sine theta equals the opposite side divided by the hypotenuse. Let us assume a triangle ABC whose and B is a right angle, and C is the theta angle.

So if sine theta is 0.5 or 1/2, it means AB=1 and AC=2.

Similarly, cosine theta equals adjacent side over hypotenuse, tangent theta equals opposite side over adjacent side, cosecant theta is hypotenuse over opposite side, secant equals hypotenuse over adjacent side, and cotangent equals adjacent side over opposite side.

Answer 2

Answer:

sin theta=0.5=1/2=sin30°

=>theta =30°

then cos theta=cos30°=√3/2

similarly tan theta =1/√3

sec theta=2/√3

cosec theta=2

cot theta =√3

according to question,

cos theta * tan theta * sec theta * cosec theta * cot theta

=(√3/2)*(1/√3)*(2/√3)*2*√3

=2