if cos theta 1/4 then find all trignometric ratios

Question

math logic

Answer 1

Pythagorean identity: sin²θ + cos²θ = 1 and this enables you to compute sine if you know cosine, or vice versa.

From there on, the rest of the trig functions are easy.

The only concern is to know what quadrant theta is in, so that the correct SIGN is chosen.

Answer 2

x² + y² = r²

1² + y² = 4²

1 + y² = 16

y² = 15

y = ±√15

 

x = 1, y = ±√15, r = 4

 

The cosine is positive in quadrants I and IV, so you need to find the values for the other trig functions in QI and QIV.   In QI, x=1, y=√15, r=4.  In QIV, x=1, y=-√15, r=4.

 

cos x = x/r = 1/4

sin x = y/r = (√15)/4 in QI and -(√15)/4 in QIV

tan x = y/x = ____ in QI and ____ in QIV

cot x = x/y = ____ in QI and ____ in QIV

sec = r/x = ____ in QI and ____ in QIV

csc x = r/y = ____ in QI and ____ in QIV