Find the exact value of the following. Please show all work in the process sin2(75°) sin 45° cos230° (Hint: sin2θ = (sinθ)2 )

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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I will answer your 1st question. You need to post the second as a separate question in terms of the eNotes rules.

Remember, when the (as in this case) 2 appears in between the sin and the theta or angle, you are effectively halving the period of the normal graph. The period of a normal sin graph is 360 degrees so this means that it is completing the cycle from beginning to end -  (the period) - in half that distance (ie 180 degrees).

You can use the formula `sin2 theta = 2 sin theta. cos theta`   or you can use your calculator. The calculator may give you 0, 48 and the formula will give you 0,5 for that part of the calculation. Sin 45 is a special angle and is either 1/square root 2 or square root 2 / 2 (they mean the same). Then cos 230 is in Quad III where cos is negative so cos (180 + 50) = 230  is - cos 50 degrees. So

sin 2 (75). sin 45. cos 230 

= `1/2`  x square root 2 / 2 x cos (180 + 50)

=  - 0,2272

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