Question

If sin Θ = 1 over 4 and tan Θ > 0, what is the value of cos Θ?

Answer 1

@jdoe0001 almost done just this and one more

Answer 2

well recall the quadrants

what signs would you get for the 1st, 2nd, 3rd and 4th quadrants for cosine and sine?

Answer 3

(+,+),(+,-),(-,-),(-,+)

Answer 4

http://www.emaths.net/articles_imgs/6906/review48.jpg <---- right

Answer 5

ok so its gonna be + cosine right

Answer 6

so we know that sine for this angle is 1/4

and the tangent is > 0, which is another way to say the tangent is positive

so if the tangent is positive, that means it has to be quadrants 1 or 3
because on 1 sine and cosine are both positive
and on 3 sine and cosine are both negative

thus \(\bf tan(\theta)=\cfrac{+}{+}\implies tan(\theta) >0\qquad Quadrant\ I
\\ \quad \\
tan(\theta)=\cfrac{-}{-}\implies tan(\theta) >0\qquad Quadrant\ III\)

Answer 7

ok :)

Answer 8

well since the sine is positive, yes, that means is on the I quadrant
so the cosine is also positive

so \(\bf sin(\theta)=\cfrac{1}{4}\to \cfrac{opposite}{hypotenuse}\to \cfrac{b=1}{c=4}
\\ \quad \\
c^2={\color{blue}{ a}}^2+b^2\implies \pm\sqrt{c^2-b^2}={\color{blue}{ a}}\qquad cos(\theta)=\cfrac{+{\color{blue}{ a}}}{c}\)

Answer 9

ok so its √15/4?

Answer 10

yeap