Review these 1.) cos-1 √3/2 2.) sin-1-√2/2 3.) tan -1 -√3 4.) cos-1 -1/2 5.) cos π/3 6.) sin 0

The Inverse Trigonometric Functions (Continued) Section 7.2 The Inverse Trigonometric Functions (Continued)

We have to use the information we know about tan-1 ½ from previous lessons!! Since tan is positive and with tangent we can only use the first or fourth quadrant so we know this is in the first quadrant. We also know that tangent is opposite (y) over adjacent (x) We used tangent to create the triangle whose angle fits and Pythagorean theorem to find the missing side. Now we can find sin using the trig ratios.

We have to use the information we know about sin-1 1/3 from previous lessons!! Since sin is negative and with sine we can only use the first or fourth quadrant so we know this is in the fourth quadrant. We also know that sin is opposite (y) over hypotenuse (r) We used sine to create the triangle whose angle fits and Pythagorean theorem to find the missing side. Now we can find cos using the trig ratios.

Write each trigonometric expression as an algebraic expression in u. Sin(cos-1 u) We have to use the information we know about cos-1 u from previous lessons!! Since cos is positive and with cosine we can only use the first or second quadrant so we know this is in the first quadrant. We also know that cosine is adjacent (x) over hypotenuse (r) Draw the triangle in the first quadrant with x = u and r = 1 Using Pythagorean Theorem we get y2 + u2 = 12 y2 = 1 – u2 y =   We used cosine to create the triangle whose angle fits and Pythagorean theorem to find the missing side. Now we can find sin using the trig ratios. 1     u