How do you find the exact values of #sintheta# and #tantheta# when #costheta=2/5#?

Answer 1

#sin theta=sqrt21/5#
#tantheta=sqrt21/2#

We need

#sin^2theta+cos^2theta=1#
#tan theta=sintheta/costheta#
#costheta=2/5#
#sintheta=sqrt(1-cos^2theta)#
#=sqrt(1-4/25)=sqrt(21/25)#
#=sqrt21/5#
#tantheta=sintheta/costheta=(sqrt21/5)/(2/5)#
#=sqrt21/2#
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Answer 2

To find the exact values of sinθ and tanθ when cosθ = 2/5, you can use the Pythagorean identity for trigonometric functions.

Given that cosθ = 2/5, you can find sinθ using the Pythagorean identity sin^2θ + cos^2θ = 1. Then, solve for sinθ.

Once you have sinθ, you can find tanθ using the relationship tanθ = sinθ / cosθ.

So, you'll find sinθ first and then use it to find tanθ.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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