vsmple 2Consider the righe triangle ABC wthere C is a right angle.Find the raties for sinA and cos B. What do you notice?Find the ratios for cos A and sin B. What do you notice?important Discovery!The acute angles in a right triangle are always complementary. The sine of any acute angleis equal to the cosine of its complement.A+B=90 iff sin A=cosBUsing the 2 equations listed above, how can we rewrite sin A = cos B in terms of one angle?

Answered: Image /qna-images/answer/b07a3e44-143f-4429-afcc-b043e9e2d8a3.jpg

Answered: Nmple 2 Cosier the ghe tr angle ABC…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter74: Introduction To Compound Angles

Section: Chapter Questions

Problem 2A

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Similar questions

a The radian measure of an angle is the length of the __________ that subtends the angle in a circle of radius _________. b To covert degrees to radians, we multiply by_______. c To convert radians to degrees, we multiply by______.
A right triangle with an angle is shown in the figure. a Label the opposite and adjacent sides of and the hypotenuse of the triangle. bThe trigonometric functions of the angle are defined as follows: sin=, cos=, tan= c The trigonometric ratios do not depend on the size of the triangle. This is because all right triangles with the same acute angle are ______________.
a Let an acute angle in a right triangle. Identify the opposite side, the adjacent side, and the hypotenuse in the figure. b Define the six trigonometric ratios in terms of the adjacent and opposite sides and the hypotenuse. c Find the six trigonometric ratios for the angle shown in the figure. d List the special values of sine, cosine and tangent.
The designers of a water park have sketched a preliminary drawing of a new slide (see figure). (a) Find the height h of the slide. (b) Find the angle of depression from the top of the slide to the end of the slide at the ground in terms of the horizontal distance d a rider travels. (c) Safety restrictions require the angle of depression to be no less than 25 and no more than 30. Find an interval for how far a rider travels horizontally.
Height of a Mountain To calculate the height h of a mountain, angles and and distance d are measured, as shown in the figure below. a Show that h=dcotcot b Show that h=dsinsinsin() c Use the formulas from parts a and b to find the height of a mountain if =25, =29 and d=800 ft. Do you get the same answer from each formula?
Circumference of the Earth The Greek mathematician Eratosthenes ca.276-195 B.C. measured the circumference of the earth from the following observations. He noticed that on a certain day the sun shone directly down a deep well in Syene modern Aswan. At the same time in Alexandria, 500 miles north on the same meridian, the rays of the sun shone at an angle of 7.2 to the zenith. Use this information and the figure to find the radius and circumference of the earth.
Refraction When you stand in shallow water and look at an object below the surface of the water, the object will look farther away from you than it really is. This is because when light rays pass between air and water, the water refracts, or bends, the light rays. The index of refraction for water is 1.333. This is the ratio of the sine of 1 and the sine of 2 (see figure). (a) While standing in water that is 2 feet deep, you look at a rock at angle 1=60 (measured from a line perpendicular to the surface of the water). Find 2. (b) Find the distances x and y. (c) Find the distance d between where the rock is and where it appears to be. (d) What happens to d as you move closer to the rock? Explain.

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