Find 𝑠𝑖𝑛𝜃 if 𝑐𝑜𝑠𝜃 = 3/4 and 𝜃 is in the fourth quadrant

Answer 1

in the 4th quadrant both sines are <0 and cosines are >0

cosx = 3/4 = adjacent side over hypotenuse

h^2 = a^2 + o^2 where h=hypotenuse, a=adjacent side, o = opposite side

o^2 = h^2 -a^2 = 4^2 -3^2 = 16-9 = 7

o = -sqr7

sinx = o/h = -sqr7/4 = about 0.6614

check the answer, by calculating the angle

cosx = 3/4

x = the angle whose cosine is 3/7 = 0.75

use a calculator with an inverse trig function

x =about + or - 41.41

sin41.41 = -0.6614

sqr7/4 = about -0.6614