Question

Each point P is on the terminal side of an angle θ.

1. P(2,9) 2. P(5, -2)

a. Draw a diagram showing θ in standard position.

b. Calculate sin θ, cos θ, and tan θ in exact values.

c. How far is P from the origin?

d. What is the value of θ?

e. Give 2 positive and 1 negative co-terminal values of θ in standard position.

Answer 1

for (2,9)
r = √(2^2 + 9^2) = √85
sinθ = y/r = 9/√85
cosθ = x/r
and so on
θ = sin^-1(9/√85) = 77.47°
co-terminals are just θ±360k° for integer values of k.

Answer 2

for a standard position angle determined by the point (x,y) what are the values of the trigonometric functions for the point (6,8) find csc theta sec theta

Answer 3

for a standard position angle determined by the point (x,y) what are the values of the trigonometric functions for the point (6,8) find csc theta sec theta

csc theta=5/4, sec theta=4/5
csc theta=5/4, sec theta=5/3
csc theta=4/5, sec theta 5/3
csc theta=4/5, sec theta 3/5

Answer 4

for a standard position angle determined by the point (x,y) what are the values of the trigonometric functions for the point (6,8) find csc theta sec theta EXPLAIN

A.csc theta=5/4, sec theta=4/5
B.csc theta=5/4, sec theta=5/3
C.csc theta=4/5, sec theta =5/3
D.csc theta=4/5, sec theta= 3/5

Answer 5

First, we need to find r, which is the distance between the origin (0,0) and (6,8):

r = √(6^2 + 8^2) = √100 = 10

Next, we can find sin, cos, tan, csc, sec, and cot:

sin θ = y/r = 8/10 = 4/5
cos θ = x/r = 6/10 = 3/5
tan θ = y/x = 8/6 = 4/3
csc θ = 1/sin θ = 5/4
sec θ = 1/cos θ = 5/3
cot θ = 1/tan θ = 3/4

Finally, we can find csc θ × sec θ:

csc θ × sec θ = (1/sin θ) × (1/cos θ) = 5/4 × 5/3 = 25/12

Therefore, csc θ × sec θ = 25/12.

Answer 6

The correct answer is:

csc theta = 5/4, sec theta = 3/5.

Answer 7

To find the correct answer, we first need to determine the reference angle for the angle determined by the point (6,8) in standard position:

r = sqrt(6^2 + 8^2) = 10

sin(theta) = 8/10 = 4/5

cos(theta) = 6/10 = 3/5

The point (6,8) is in the second quadrant, so the reference angle will be:

theta_ref = pi/2 - sin^-1(4/5) = pi/2 - 0.93 = 0.64

Therefore, the values of the trigonometric functions for an angle which contains the point (6,8) in standard position are:

sin(theta) = sin(pi - theta) = -sin(0.64) ≈ -0.60

cos(theta) = cos(pi - theta) = -cos(0.64) ≈ -0.79

tan(theta) = tan(pi - theta) = sin(0.64) / -cos(0.64) ≈ 0.76 / -0.65 ≈ -1.17

csc(theta) = 1 / sin(theta) ≈ -1.67 / -0.60 ≈ 2.78

sec(theta) = 1 / cos(theta) ≈ -1.26 / -0.79 ≈ 1.59

cot(theta) = 1 / tan(theta) ≈ -0.87 / 0.76 ≈ -1.15

Therefore, the correct answer is option D. csc theta = 4/5, sec theta = 3/5.