Trigonometric Functions TANGENT, SINE, COSINE

TANGENT - Definition Tangent of an acute angle is the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. Tangent ratio is formed by the legs of a right triangle Written as tanA tan 𝐴= 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑒𝑔 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑛𝑔𝑙𝑒 𝐴 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑒𝑔 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝐴 = 𝑎 𝑏 Tangent ratio is constant for a given angle A C B a b c

TANGENT - Examples Find the tangent of angle J. Find the tangent of angle K. tan 𝐾= 10 24 =0.417 K L J 10 24 26

SINE - Definition Sine of an acute angle is the ratio of the length of the leg opposite the angle to the length of the hypotenuse of the right triangle. Sine ratio is formed by a leg and the hypotenuse of a right triangle Written as sinA sin 𝐴= 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑒𝑔 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑛𝑔𝑙𝑒 𝐴 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 𝑎 𝑐 Sine ratio is constant for a given angle A C B a b c

SINE - Examples Find the sine of angle J. Find the sine of angle K. 10 24 26

COSINE - Definition Cosine of an acute angle is the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse of the right triangle. Cosine ratio is formed by a leg and the hypotenuse of a right triangle Written as cosA cos 𝐴= 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑒𝑔 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝐴 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 𝑏 𝑐 Cosine ratio is constant for a given angle A C B a b c

COSINE - Examples Find the cosine of angle J. Find the cosine of angle K. cos 𝐾 = 24 26 =0.923 K L J 10 24 26

SOH CAH TOA Sine Hypotenuse Cosine Hypotenuse Tangent Adjacent Opposite Adjacent Opposite sin= 𝑂𝑃𝑃𝑂𝑆𝐼𝑇𝐸 𝐻𝑌𝑃𝑂𝑇𝐸𝑁𝑈𝑆𝐸 cos = 𝐴𝐷𝐽𝐴𝐶𝐸𝑁𝑇 𝐻𝑌𝑃𝑂𝑇𝐸𝑁𝑈𝑆𝐸 tan = 𝑂𝑃𝑃𝑂𝑆𝐼𝑇𝐸 𝐴𝐷𝐽𝐴𝐶𝐸𝑁𝑇