Question

Suppose è is an acute angle of a right triangle. For this function, find the values of the remaining five trigonometric functions of è. Round to four decimal places.
sin è = 0.1
cos è =
tan è =
cot è =
csc è =
sec è =

Answer 1

If you use a calculator with an inverse sine function, you can enter sin^-1 (0.1) = and find out what the acute angle value is. Then you can use that and plug it into the cos, tan, cot, csc, and sec functions of your calculator.

If you don't have a calculator, use this fact: (cos a)^2 + (sin a)^2 = 1.

Solve to find (cos a)^2 = 1 - (sin a)^2
so cos a = sqrt (1 - [sin a]^2) = sqrt (1 - (0.1)^2) = sqrt (1 - 0.01) = sqrt 0.99.

Then you can find tan a = sin a / cos a.

The other ratios are reciprocals. You can find formulas for them in your text and use the above results in your calculations.