Chapter 10 Trigonometric Identities and Equations Flashcards
(26 cards)
What is costheta for a point P(x, y) on a unit circe when theta is acute?
Costheta is the x-coordinate of P
What is sintheta for a point P(x, y) on a unit circe when theta is acute?
Sintheta is the y-coordinate of P
What is tantheta for a point P(x, y) on a unit circe when theta is acute?
Tantheta is the gradient of OP (y/x)
What range of angles lie in the first quadrant of a unit circle?
0 to 90
-270 to -360
What range of angles lie in the second quadrant of a unit circle?
90 to 180
-180 to -270
What range of angles lie in the third quadrant of a unit circle?
180 to 270
-90 to -180
What range of angles lie in the fourth quadrant of a unit circle?
270 to 360
-90 to 0
What is the exact value of sin30?
1/2
What is the exact value of sin60?
sqrt3/2
What is the exact value of cos30?
sqrt3/2
What is the exact value of cos60?
1/2
What is the exact value of tan30?
1/sqrt3 or sqrt3/3
What is the exact value of tan60?
sqrt3
What is the exact value of sin45?
1/sqrt2 or sqrt2/2
What is the exact value of cos45?
1/srt2 or sqrt2/2
What is the exact value of tan45?
1
What is the equation of the unit circle?
x^2 + y^2 = 1
What is the trigonometric identity for sin^2x + cos^2x?
sin^2x + cos^2x = 1
What is the trigonometric identity for tanx?
sinx/cosx = tanx
When do solution for sinx = k and cosx = k exist?
When -1 <= k <= 1
When do solutions for tanx = p exist?
For all values of p
What are sintheta, costheta and tantheta for an angle in the first quadrant?
sintheta, costheta and tantheta are all positive
What are sintheta, costheta and tantheta for an angle in the second quadrant?
Only sintheta is positive
What are sintheta, costheta and tantheta for an angle in the third quadrant?
Only tantheta is positive
