1. 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

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

3. 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