If cos θ = negative 4 over 7, what are the values of sin θ and tan θ?

Solution:

It is given that

cos θ = negative 4 over 7

We can write it as

cos θ = -4/7

Let us make use of the trigonometric identity

sin² θ = 1 - cos² θ

Substituting the value of cos θ

sin² θ = 1 - (-4/7)² = 1 - 16/49

By further calculation

sin² θ = (49 - 16)/49

sin² θ = 33/49

sin θ = ± √33/7

As cos θ is negative, θ should be in II and III quadrants where both the values are accepted.

tan θ = sinθ/ cos θ = ± √33/7 (-7/4) = ± √33/4

Therefore, the values of sin θ and tan θ are ± √33/7 and ± √33/4.

If cos θ = negative 4 over 7, what are the values of sin θ and tan θ?

Summary:

If cos θ = negative 4 over 7, the values of sin θ and tan θ are ± √33/7 and ± √33/4.