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# sinӨ, if cosӨ=2/5 and tan Ө<0 evaluate?

sinӨ, if cosӨ=2/5 and tan Ө<0 how do i work this out?

### 6 Answers

- Anonymous9 years agoFavorite Answer
From the cosine information we have a triangle whose X leg is 2 and whose hypotenuse is 5. The length of the Y leg is therefore sqrt(25-4) = sqrt(21).

Since the tangent is negative we know that the angle is in quadrant IV and the sine must also be negative. Hence the sine of the angle is -sqrt(21)/5

- Anonymous9 years ago
use

sin^2 + cos^2 = 1

- Martin FLv 69 years ago
Draw a right triangle representing cosӨ = 2/5 . . . (adjacent = 2 / hypot = 5)

Use pythag to find 'opposite' . . .

Find sinӨ (opposite / hypot).

- s kLv 79 years ago
sin(x)^2 + cos(x)^2 = 1

So sin(x) = ±√(1 - cos(x)^2)

= ±√(1 - 4/25)

= ±√(21/25)

= ±√(21)/5

As tan(x) < 0 and cos(x) > 0, we must have sin(x) < 0.

So sin(x) = -√(21)/5.

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- Anonymous9 years ago
sinӨ^2 + cosӨ^2=1

sinӨ^2 + 4/25=1

sinӨ^2=21/25

sinӨ= sqrt(21)/5

sinӨ= -4.582/5

sinӨ= -0.9165