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    2023-01-12T20:49:41+00:00

    Write The Expression As The Sine, Cosine, Or Tangent Of An Angle. Cos 96° Cos 15° + Sin 96° Sin 15°

    For those of us who have studied trigonometry, we are familiar with the three main trigonometric functions: sine (sin), cosine (cos), and tangent (tan). These three functions are used to calculate angles in a triangle and can also be used to write an expression as either a sine, cosine, or tangent of an angle. In this blog post, we will look at how to write an expression as the sine, cosine, or tangent of an angle. Specifically, we’ll use the example of writing the expression: “cos 96° cos 15° + sin 96° sin 15°” as the sine, cosine, or tangent of an angle.

    What is the sine, cosine, and tangent of an angle?

    The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

    How to write the expression as the sine, cosine, or tangent of an angle

    To write the expression as the sine, cosine, or tangent of an angle, we use the following trigonometric identities:

    sin(x) = cos(x-90°)
    cos(x) = sin(x+90°)
    tan(x) = cos(x)/sin(x)

    For example, if we want to write the expression “3cos60° + 4sin60°” as the sine of an angle, we would use the identity sin(x) = cos(x-90°):

    3cos60° + 4sin60° = sin(60°-90°) + 4sin60° = sin(-30°) + 4sin60° = -0.5 + 0.86603… = 0.36603…

    The different types of angles

    There are three different types of angles: acute, obtuse, and right.

    Acute angles are less than 90 degrees. Obtuse angles are greater than 90 degrees. Right angles are exactly 90 degrees.

    Practice problems

    Assuming you want a detailed answer for the subheading “1. Practice problems” and not the whole blog article:

    1. Practice Problems
    Now that we’ve gone over the basics of working with trigonometric functions, let’s do some practice problems. Remember, if you get stuck on any of these, go back and review the corresponding section in this post.

    Problem 1: Write the expression as the sine, cosine, or tangent of an angle.
    cos ° cos ° + sin ° sin °

    This can be rewritten as follows:
    (cos30cos60)+(sin30sin60)
    = (1/2)(sqrt(3)/2)+((1/2)(1/2)) = (1/2)(sqrt(3)/2)+(1/4) = ((sqrt(3))/4)+(1/4) = (sqrt(3)+1)/4

    Conclusion

    In this exercise, we have successfully written the expression as a combination of sine, cosine, and tangent functions of angles. We used simple trigonometry rules to break down the expression into manageable parts and then recombined them to form an equivalent expression. This highlights one of the most important principles in mathematics: that any problem can usually be broken down into simpler pieces so that it is easier to solve.

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