The document discusses trigonometric functions of an acute angle in a right triangle. It defines the six trig functions (sine, cosine, tangent, cotangent, secant, cosecant) in terms of the sides of the right triangle. It then gives an example of calculating the trig functions of angle A in a right triangle where the lengths of sides a and b are given.

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. 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. 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. 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. 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. 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. 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. 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’