6. [-/5 Points] DETAILS LARPCALCLIM4 4.3.009. MY NOTES ASK...

6. [-/5 Points] DETAILS LARPCALCLIM4 4.3.009. MY NOTES ASK YOUR TEACHER Find the exact values of the six trigonometric functions of the angle ? shown in the figure. sin(?) = cos(?) = tan(?) = csc(?) = sec(?) = cot(?) = 6. [-/5 Points] DETAILS LARPCALCLIM4 4.3.014. MY NOTES ASK YOUR TEACHER Find the exact values of the six trigonometric functions of the angle ? for each of the two triangles. Explain why the function values are the same.

Transcript

00:01 So in the given question we are having a right angled triangle and we are told we are given that the vertical distance of one side of this triangle is four the horizontal distance is four the hypotenuse of the triangle is not given we know that the triangle is right angled the angle over here is given as theta and we are to find all the trigonometric ratios of this triangle.

00:35 So first let's find the hypotenuse and this can be done according to the pythagorean theorem, right? so according to the pythagorean theorem, what it says is that if we have a right angled triangle, if we have a right angled triangle with sides say a and b and we have the hypotenuse the hypotenuse can be found by taking the square root of the sum of squares of a and b that is square root of a square plus b square so over here the hypotenuse would be having a value which is equal to square root of four square plus four square which would be equal to 16 plus 16 that is 32 which we can write as 16 times 2 so this would be equal to 4 times square root of 2 so this is the length of the high port news so now next thing that we need to know is we need to find the angle of sine theta cos theta and tan theta from the triangle so when we take sine theta from this triangle what we do is we take let's say this as theta, we take the opposite side to the angle theta and divide it with the hypotenuse.

02:08 If it is cos theta, we take the adjacent side and divide it with the hypotenuse.

02:13 And for the last ratio, tan theta, we take the opposite side to the angle theta and divide it with the adjacent side to angle theta.

02:22 So these are the formulas or the method that we normally use.

02:28 If we have a right angle triangle in order to find the trigonometric ratios of the angles in the triangle so keeping this in mind sine theta would be equal to 4 divided by 4 root 2 which would be equal to 1 root 1 by square root of 2 cost theta would be having the same value tan theta would then be equal to to 1 since sine theta and cos theta have equal values.

03:03 Now for seek theta we can simply take the value as 1 by cost theta which would be equal to square root of 2...

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