7.4 - The Primary Trigonometric Ratios Determine the values of the tangent, sine and cosine ratios for Angle A and Angle B to four decimal places. A For Angle A (67o), Opposite = a Adjacent = b Hypotenuse = c c 67o b 23o B a C sin(67o) = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 𝑎 𝑐 =𝟎.𝟗𝟐𝟎𝟓 cos(67o) = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 𝑏 𝑐 =𝟎.𝟑𝟗𝟎𝟕 tan(67o) = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 = 𝑎 𝑏 =𝟐.𝟑𝟓𝟓𝟗 SOH-CAH-TOA

Example #2 Determine the measure of 𝜃 to the nearest degree, using the sine primary trigonometric ratio. sin𝜃 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 2.00 5.39 𝜃= sin −1 2.00 5.39 𝜃≅ 21.8o ≅ 22o 5.39 cm 2.00 cm 𝜃 x

In Summary… The primary trigonometric ratios for Angle A are sin A, cos A and tan A If angle A is one of the acute angles in a right triangle, the primary trigonometric ratios can be determined using the the ratios of the sides Using the Pythagorean Theorem, opposite2 + adjacent2 = hypotenuse2 in any right triangle