Project (Special Right Triangles: A right triangle is composed of a right…
(Special Right Triangles: A right triangle is composed of a right angle the angle at C, and two acute angles which are angles less than a right angle. Angle θ is formed by hypotenuse and side BC
, Radians and Degrees: Standard unit of angular measure. The length of an arc of a unit circle is numerically equal to measurement in radians of the angle that it subtends
, Terminal, Coterminal, and Reference Angles: If measured in a clockwise direction the measurement is negative.
, Sine: the sine of an acute angle is defined in the context of a right triangle: it is the ratio of the length of the longest side or the hypotenuse.
Cosine: the cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse.
Tangent: the tangent of an angle is the length of the opposite side divided by the length of the adjacent.
, Cotangent: The ratio of the hypotenuse to the shorter side adjacent to an acute angle the angle
Secant: The ratio of the hypotenuse to the shorter side adjacent to an acute angle the reciprocal of a cosine
Cosecant: The ratio of the hypotenuse to the side opposite an acute angle; the reciprocal of sine
, Create and Solve a real world problem using trig: Finding the height of a balloon.
Distance from you to the bottom of the balloon is 2000 feet and looking up at the balloon is 30 degrees.
Tan 30 degrees= (y/2000)
2000 tan 30 degrees=y
, Unit Circle: The unit circle is used to understand sines and cosines of angles found in right triangles. The unit circle has a center at the origin (0,0) and a radius of one unit. Angles are measured starting from the positive x-axis in quadrant I and continue around the circle. The ray from the origin point on the circle (x,y) is a point, if the ray from origin (0,0) to (x,y) makes an angle from the positive x-axis then
, Positive and Negative Angles: Positive angle is created by rotating counter clockwise around the origin.
, Evaluate Reciprocal Relationship Between Pairs of Trig Functions: Since of θ =opp/hyp
Cosine of θ =adj/hyp
Tangent of θ =opp/adj
Cosecant of θ =hyp/opp
Secant of θ =hyp/adj
Cotangent of θ =adj/opp
, t= π
sin60= (y/r)= √3/2