HELP SOLVE AG TRIG PROBLEMS A Length of a shadow If a tree 2

HELP SOLVE A-G TRIG PROBLEMS. A. Length of a shadow If a tree 20 ft tall casts a shadow 8 ft long, how long would the shadow of a 30 ft tree be at the same time and place?

B. Find the values of the six trigonometric functions for an angle in standard position having each given point on its terminal side. (6sqrt3, -6)

C. In Exercises 35 and 36, consider and angle theta in standard position whose terminal side has the equation y = -5x, with x less than or equal to 0.

D. Sketch theta and use an arrow to show the rotation if 0° less than or equal to theta less than 360°.

E. Find the exact values of sin , cos , tan , cot , cot , sec , and csc ,.

F. Decide whether each statment is possible or impossible for some angle theta. (a) sec theta = -2/3 (b) tan theta = 1.4 (c) cos theta = 5

G) Find all six trigonometric function values for each angle theta. Rationalize denominators when applicable. sec theta = -sqrt5, and theta is in quadrant 2.

SHOW ALL WORK AND ANSWER ALL PLEASE.

Solution

20ft tree casts a shadow of 8 ft long

lets say 30 ft tree would cast x ft long

20/30 = 8 / x

x = 8* 30 / 20

x = 12 feet

therefore, 30 feet tree will cast a shadow of 12 feet

2) point is ( 6 sqrt 3 , -6 )

it lies in 4th quadrant

length of hypotenuse = sqrt ( 144) = 12

sin theta = -6 / 12 = -1/2

cos theta = 6 sqrt 3 / 12 = sqrt 3 / 2

tan theta = - 6 / 6 sqrt 3 = - sqrt 3 / 3

csc theta = 1/ sin theta = -2

sec theta = 1/ cos theta = 2 / sqrt 3 = 2 sqrt 3 / 3

cot theta = - sqrt 3