If sinθ=5/13,determine each of the following without the use of a calculator

(Hint use a sketch)(θ<90°)
1.4.1 cos θ
1.4.2 tanθ

1 answer

sinθ=5/13 = y/r
so sketch a right-angled triangle with hypotenuse 13, opposite side (the y)
equal to 5.
x^2 + y^2 = r^2
x^2 + 25 = 169
x^2 = 144
x = 12 , everything is positive since we are in quadrant I

cosθ = 12/13
tanθ = 5/12

perhaps you recognized the common 5-12-13 right-angled triangle.