Sketch a right triangle that satisfies csc(θ) = 3/2. Then find the exact values of the remaining 5 trigonometric functions.

Question

Sketch a right triangle that satisfies csc(θ) = 3/2. Then find the exact values of the remaining 5 trigonometric functions.

Answer 1

cscA = 1/sinA = 3/2

sinA =2/3= 0.6667

sin60 = sqr3 = 1.732

sin30 = 1/2

sin45 = 1/sqr2 = sqr2/2 = 1.414/2 = 0.707 > 0.667

so the angle is slightly smaller than 45 degrees

Use the calculator to find the other trig functions

sec, tan, cot, cos

use a calculator or tables to get a more precise answer

use the inverse sine function on a calculator

or the inverse cosecant function

A=-41.810 degrees with a calcuator

use a calculator to find the other trig functions, secant, tangent, cotangent and cosine

If the height of the right triangle is 2 with hypotenuse 3, then the base of the triangle is square root of 3^2 - 2^2 = square root of 5, about 2.23. use a calculator to get more decimal places

for a sketch plot the point (2.2,23) on a graph. drop a vertical downward from that point to the x-axis at (2.2,0), connect the point (2.,2.23) to the origin, that's the hypotenuse.