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# Trigonometry

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### Trigonometry

1. 1. Trigonometric functions of an acute angle in a right triangle. c a b C A B Leg adjacent to < A Leg opposite to <A hypotenuse It is possible to form 6 different ratios with the sides of the right triangle. Lets analyze the angle A of the right triangle in the next figure.
2. 2. Trigonometric functions of an acute angle in a right triangle. sine of < A = a c cosine of < A cos A tangent of < A tan A cotangent of < A cot A secant of < A sec A cosecant of < A csc A c a b C A B = leg opposite to <A hypotenuse = leg adjacent to <A hypotenuse = leg opposite to <A leg adjacent to <A = leg adjacent to <A leg opposite to <A = hypotenuse leg adjacent to <A = hypotenuse leg opposite to <A sin A = b c = a b = b a = c b = c a
3. 3. Trigonometric functions of an acute angle in a right triangle. If sin and cos ; find tan and cot . 3 5 4 3 3 4 4
4. 4. Problem: Find the value of each one of the trigonometric functions of the acute angle A in the right triangle ABC, if the length of the legs a and b are 60 and 91 cm respectively. B sinA= cosA= tanA= cotA= secA= cscA= 109 cm C= ? 109 C A a= 60 b=91
5. 5. Values of trigonometric functions of an acute angle. Find the value of the next functions a) sin 34°40’ b) cos 72° c) tan 55°20’ 0.568 0.309 1.446 SIN 3 ° ‘ “ 4 ° ‘ “ EXE 4 0
6. 6. Values of trigonometric functions of an acute angle. Find the value of the angle a) Sin A = 0.4181 b) Cos B = 0.6345 c) Tan A = 1.1257 24°43’ 57°36’ 48°23’ 2nd SIN 1 SHIFT EXE . 4 8 1 ° ‘ “
7. 7. Determination of right triangles If you wish to fasten a 8 m high pole using a wire tie rod held at the top of the pole and at a distance of 5 m. from the base of the pole on a horizontal ground. What should be the inclination of the wire with respect to the ground? d=5 m h=8 m H L D 1.- Make a draw and identify the data in it. 2.- Which is the information they are asking you? 3.- Find a trigonometric function that involves the information given and the missing one. 4.- Isolate the variable and find the value. Measure of the angle H tan H= opposite / adyacent tan H= 8m / 5m In this case you are locking for the angle H, so you do not need to isolate it. tan H= 8m / 5m = 1.6 <H=57°59’40” H
8. 8. Determination of right triangles The triangle ABC, where <A=35°10’ and c= 72.5, find the measure of: a) <B, b) side a. A C B 72.5 35°10´ 1.- Make a draw and identify the data in it. 2.- Which is the information they are asking you? 3.- Find a trigonometric function that involves the information given and the missing one. Measure of the angle B and side a sin A= opposite / hypotenuse Sin 35°10’= a / 72.5m a b c B a 4.- Isolate the variable and find the value. <B=90-<A (Sin 35°10’)(72.5m)= a (0.5759)(72.5m)= a 41.756= a <B=90°-35°10’ <B=54°50’