# Inverse Trigonometric Functions - Solving for an angle using Inverse Sine Function

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Language: English

Type: Robot

Number of phrases: 72

Number of words: 465

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Subtitles generated by robot
00:01
hi for today's video we're going to solve a situational problem from the concept of projectile motion using inverse trig function the problem is if an object is directed in an angle theta with theta element of closed interval 0 to pi over 2 then the range will be r is equals to v sub 0 squared over g times sine 2 theta in feet where v sub 0 in feet per second is the initial speed
00:31
and g is equals to 32 feet per second squared is the acceleration due to gravity at what angle should the object be directed so that the range will be 100 feet given that the initial speed is v sub zero is equals to 80 feet per second the given are as follows r is equals to 100 feet where r represents the range v sub 0 is equals to 80 feet per second where it represents the initial speed
01:02
and g is equals to 32 feet per second squared which is the acceleration due to gravity to solve for this problem let us plug in the given values to the formula provided to find the angle the formula is r is equals to v sub 0 squared over g times sine 2 theta substitute 100 to r 8 a squared to v sub 0 squared 32 to g it will be 100 is equals to 80
01:36
squared over 32 times sine 2 theta multiply both sides by 32 over 80 squared now let us reduce the 8 squared on the right side of the equation and then reduce the numbers with the gcf 32 it would be 32 over 80 squared times 100 is equals to sine 2 theta cancelling the term on the right side for the left side of the equation multiply 32 over 80 squared with 100 or
02:10
100 over 1 in fraction the product will be 3 200 over 80 squared evaluate the power it will be 3 200 over four hundred reduce the fraction with three thousand two hundred the product shall be one half is equals to sine two theta the final step is to swap the sides of the equation sine 2 theta is equals to one-half but we are not yet done what we have accomplished is simply the value of sine
02:44
2 theta but not the angle which is represented by theta to solve for the remaining problem we shall use the inverse function of sine two theta is equals to inverse sine of one half calculate two theta is equals to pi over six divided by two the answer will be theta is equals to pi over 12 or 15 degrees so the answer will be the object shall
03:14
be directed at an angle of 15 degrees