Question

If cos theta=1/3 now find the value of sin theta.

Answer 1

Step-by-step explanation:

√2/√3

is the right answer

Answer 2

Concept

There is a trignometric identity, derived from the pythagoras theorem, that we need to know in order to solve this question. The identity is as follows -

cos^2a + sin^2a = 1

Given

cos ∅ = 1/3

Find

we need to find the value of sin ∅

Solution

We have cos ∅ = 1/3

we know that cos^2a + sin^2a = 1

Here cos^2∅ = (1/3)^2

cos^2∅ = 1/9

Now,

cos^2∅ + sin^2∅ = 1

1/9 + sin^2∅ = 1

sin^2∅ = 1 - 1/9

sin^2∅ = (9-1)/9

sin^2∅ = 8/9

sin∅ = sqrt(8/9)

sin∅ = {2sqrt(2)}/3

Hence, the value of sin∅ is $\frac{2\sqrt{2} }{3}$

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