Chapter 10 Trigonometric Identities and Equations

Question 1

What is costheta for a point P(x, y) on a unit circe when theta is acute?

Answer 1

Costheta is the x-coordinate of P

Question 2

What is sintheta for a point P(x, y) on a unit circe when theta is acute?

Answer 2

Sintheta is the y-coordinate of P

Question 3

What is tantheta for a point P(x, y) on a unit circe when theta is acute?

Answer 3

Tantheta is the gradient of OP (y/x)

Question 4

What range of angles lie in the first quadrant of a unit circle?

Answer 4

0 to 90
-270 to -360

Question 5

What range of angles lie in the second quadrant of a unit circle?

Answer 5

90 to 180
-180 to -270

Question 6

What range of angles lie in the third quadrant of a unit circle?

Answer 6

180 to 270
-90 to -180

Question 7

What range of angles lie in the fourth quadrant of a unit circle?

Answer 7

270 to 360
-90 to 0

Question 8

What is the exact value of sin30?

Answer 8

1/2

Question 9

What is the exact value of sin60?

Answer 9

sqrt3/2

Question 10

What is the exact value of cos30?

Answer 10

sqrt3/2

Question 11

What is the exact value of cos60?

Answer 11

1/2

Question 12

What is the exact value of tan30?

Answer 12

1/sqrt3 or sqrt3/3

Question 13

What is the exact value of tan60?

Answer 13

sqrt3

Question 14

What is the exact value of sin45?

Answer 14

1/sqrt2 or sqrt2/2

Question 15

What is the exact value of cos45?

Answer 15

1/srt2 or sqrt2/2

Question 16

What is the exact value of tan45?

Answer 16

1

Question 17

What is the equation of the unit circle?

Answer 17

x^2 + y^2 = 1

Question 18

What is the trigonometric identity for sin^2x + cos^2x?

Answer 18

sin^2x + cos^2x = 1

Question 19

What is the trigonometric identity for tanx?

Answer 19

sinx/cosx = tanx

Question 20

When do solution for sinx = k and cosx = k exist?

Answer 20

When -1 <= k <= 1

Question 21

When do solutions for tanx = p exist?

Answer 21

For all values of p

Question 22

What are sintheta, costheta and tantheta for an angle in the first quadrant?

Answer 22

sintheta, costheta and tantheta are all positive

Question 23

What are sintheta, costheta and tantheta for an angle in the second quadrant?

Answer 23

Only sintheta is positive

Question 24

What are sintheta, costheta and tantheta for an angle in the third quadrant?

Answer 24

Only tantheta is positive

Question 25

What are sintheta, costheta and tantheta for an angle in the fourth quadrant?

Answer 25

Only cos theta is positive

Question 26

What are the ranges for principal values from a calculator?

Answer 26

Cos^-1 in the range 0 <= theta <= 180
Sin^-1 in the range -90 <= theta <= 90
Tan^-1 in the range -90 <= theta <= 90