Bell Work R Find the 6 trig functions for <R. sin R = csc R = cos R = sec R = tan R = cot R = 22 cm S T 14 cm

5-3 Trigonometric Functions on the Unit Circle

More Special Triangles…Find the missing sides. 1 1 ? ? 45° 60° ? ?

Our Goal today is to learn to use the Unit Circle to evaluate values of angles The Unit Circle: A circle with a radius of 1 that is placed on the xy coordinate plane with center at the origin.

More Unit Circle Find the sine, cosine, and tangent of a 30° angle using the unit circle. Sin 30° = Cos 30° = Tan 30° = Always draw the triangle to the x axis!!! Always write the ordered pair, and the answer is in that point!!!!

More Unit Circle Find the sine, cosine, and tangent of a 60° angle using the unit circle. Sin 60° = Cos 60° = Tan 60° = Always draw the triangle to the x axis!!! Always write the ordered pair, and the answer is in that point!!!!

More Unit Circle Find the sine, cosine, and tangent of a 45° angle using the unit circle. Sin 45° = Cos 45° = Tan 45° = Always draw the triangle to the x axis!!! Always write the ordered pair, and the answer is in that point!!!!

More Unit Circle Find the sine, cosine, and tangent of a 210° angle using the unit circle. Sin 210° = Cos 210° = Tan 210° = Always draw the triangle to the x axis!!! Always write the ordered pair, and the answer is in that point!!!!

More Unit Circle Find the sine, cosine, and tangent of a 150° angle using the unit circle. Sin 150° = Cos 150° = Tan 150° = Always draw the triangle to the x axis!! Always write the ordered pair, and the answer is in that point!!!!

More Unit Circle Find the sine, cosine, and tangent of a 600° angle using the unit circle. Sin 600° = Cos 600° = Tan 600° = Always draw the triangle to the x axis!! Always write the ordered pair, and the answer is in that point!!!!

More Unit Circle Find the sine, cosine, and tangent of a 225° angle using the unit circle. Sin 225° = Cos 225° = Tan 225° = Always draw the triangle to the x axis!! Always write the ordered pair, and the answer is in that point!!!!

More Unit Circle Find the sine, cosine, and tangent of θ using the unit circle. Sin θ = y/1 = y Cos θ = x/1 = x Tan θ = y/x These are always the ratios for an angle on the unit circle….but remember that the radius must be 1!!!

Signs in Each Quadrant. All Student Take Calculus (-, +) (+, +) (-, -) (+, -)

Find each value using the Unit Circle. Cos 210° Sin 300° Cos 135 ° Tan 480°

Build the Unit Circle

What about Reciprocal Functions? Csc θ = 1/y (reciprocal of Sin θ) Sec θ = 1/x (reciprocal of Cos θ) Cot θ = x/y (reciprocal of Tan θ)

Find each value using the Unit Circle. Sec -135° Csc 660° Cot 240 ° Sec -225°

What about Quadrantal Angles? Sin 90° Cos 90° Tan 90 ° Csc 90 ° Sec 90 ° Cot 90 °

Find each value using the Unit Circle. csc 270° Sin -225° Cot 495 ° Sec -240°

Values not on the unit circle. Day 2 Values not on the unit circle.

Finding trig values when it is NOT a unit circle. (Radius is not one) Trig Ratios Sin θ = Csc θ = Cos θ = Sec θ = Tan θ = Cot θ =

Sin θ = Csc θ = Cos θ = Sec θ = Tan θ = Cot θ = Find the values of the six trig functions for angle θ in standard position if a point with coordinates (5, -12) lies on its terminal side. Sin θ = Csc θ = Cos θ = Sec θ = Tan θ = Cot θ = Always draw the triangle to the x axis!!!

Sinθ= Csc θ= Cosθ= Sec θ = Tanθ= Cot θ= Find the values of the six trig functions for angle θ in standard position if a point with coordinates (-3, -4) lies on its terminal side. Sinθ= Csc θ= Cosθ= Sec θ = Tanθ= Cot θ= Always draw the triangle to the x axis!!!

Sinθ= Csc θ= Cosθ= Sec θ = Tanθ= Cot θ= Find the values of the six trig functions for angle θ in standard position if a point with coordinates (-4, 2) lies on its terminal side. Sinθ= Csc θ= Cosθ= Sec θ = Tanθ= Cot θ= Always draw the triangle to the x axis!!!

Sinθ= Cscθ= Cosθ= Secθ= Tanθ= Cotθ = Suppose θ is an angle in standard position whose terminal side lies in Quadrant III. If sin θ = -4/5, find the values of the remaining five trig functions. Sinθ= Cscθ= Cosθ= Secθ= Tanθ= Cotθ =

Sinθ= Csc θ= Cosθ= Secθ= Tanθ= Cotθ= Suppose θ is an angle in standard position whose terminal side lies in Quadrant IV. If sec θ = √3, find the values of the remaining five trig functions. Sinθ= Csc θ= Cosθ= Secθ= Tanθ= Cotθ=