trigonometric functions

Question

Find the values of the trigonometric functions of t from the given information.

Answer 1

"sohcahtoa"

The way I learned this was that rhyming word, supposedly an Indian word, but that might not be PC today.

But it sticks in your mind. things that rhyme tend to be easier to remember.

soh is for sinx = opposite side divided by hypotenuse

cah is for cosx = adjacent side divided by hypotenuse

toa is for tanx = opposite side divided by hypotenuse

then

cscx = 1/sinx = hypotenuse divided by opposite side

secx = 1/cosx = hypotenuse divided by adjacent side

cotx = 1/tanx = adjacent side divided by opposite side

draw a unit circle, a right triangle with the given information,

given information may be a point on the circle, or an angle

then calculate each of the 6 trig functions

or sometimes you are just given one trig value and then calculate the other 5 trig functions.

It generally helps to have a picture, by graphing the angle on a unit circle or plot the given point and construct a right triangle with it as the top right vertex of the triangle. The make the "sohcahtoa" calculations.

For example, you're given the point (-3,4). It's graphically in quadrant II, with an angle between pi/2 and pi, or in degrees it's between 90 and 180.

construct a right triangle with sides -3 as the adjacent side and 4 as the opposite side, and sqr(3^2+4^2) = 5 as the hypotenuse. Then sinx =4/5, cosx = -3/5, tanx =4/-3 = -4/3, secx =1/cosx = -5/3, cscx = 5/4 cotx =-3/4

it sometimes helps to check your answer by finding the angle x with a calculator

that has inverse trig functions

plug in 4/5 or .8

then do the inverse sine, sin^-1(.8) = about 53.13 but that's the reference angle in quadrant I. You want quadrant II, so if you use 53.13, check the signs when you make the other trig calcuations, with sinx and cscx >0, cosx and secx <0, tanx and cotx<0

then find cos53.13 = about 0.6 which is the same as 3/5, but make it negative -3/5