How to find the exact value of a trig function?

There is no definitive answer to the question “How to find the exact value of a trig function?” However, a few methods that could be used to find the exact values of trig functions without a calculator include using trigonometric identities, graph paper, or a reference book.

How to find the exact value of a trig function?

There is no general process for finding the exact value of a trig function. However, there are some special cases where the exact value can be determined. For example, the value of sin(pi/2) is 1 and the value of cos(0) is 1. In general, to find the exact value of a trig function, one would need to use a special function such as the inverse trig function.

The exact value of a trig function can be found using a variety of different trig function identities.

One way to find the exact value of sin(x), for example, is to use the identity sin(x) = cos(π/2 – x). So, if we want to find the value of sin(π/6), we can first calculate the value of cos(π/2 – π/6).

We know that cos(π/2) = 1, and since cos is a periodic function with a period of 2π, we also know that cos(π/2 – π/6) = cos(5π/6).

We can then use a cosine angle addition formula to simplify this further: cos(5π/6) = cos(π/2 + π/6) = cos(π/2)cos(π/6) – sin(π/2)sin(π/6) = cos(π/6) – sin(π/6). Therefore, sin(π/6) = cos(π/6) – sin(π/6), and the exact value of sin(π/6) is 1/2 – √3/2.

There are a variety of different identities that can be used to find the exact value of a trig function, and which identity to use will depend on the particular angle that is being considered.

Here are some common trig function identities:

• sin(x) = cos(π/2 – x)
• cos(x) = sin(π/2 – x)
• tan(x) = 1/tan(π/2 – x)
• sin(x) = 1/csc(x)
• cos(x) = 1/sec(x)
• tan(x) = 1/cot(x)
• sec(x) = 1/cos(x)
• csc(x) = 1/sin(x)
• cot(x) = 1/tan(x)

How do you find the exact values of trig functions without a calculator?

Additionally, many trig functions can be graphed using graph paper. By carefully plotting points and drawing a line of best fit, the exact value of a trig function can often be determined without the use of a calculator.

Some trigonometric identities that could be used to find the exact values of trig functions include the following:

• For any angle θ, sin(θ) = cos(90° – θ)
• For any angle θ, cos(θ) = sin(90° – θ)
• And For any angle θ, tan(θ) = cot(90° – θ)
• For any angle θ, cot(θ) = tan(90° – θ)

Finally, many trig function values are listed in standard reference books such as math dictionaries or tables. By consulting one of these resources, the exact value of a trig function can often be found without the use of a calculator.

Read also: How to find the area of a composite figure?

How do you calculate the surface area of a rectangular prism?

Surface Area of a Rectangular Prism A rectangular prism has six faces, so we need to find the area of all six faces and add them together. We can use the formula for the area of a rectangle to find the areas of the top and bottom faces. The formula for the area of a rectangle is A=lw, so the area of the top is A=lw=34=12.

Suzanna N. Alejos

I am Suzanna Alejos. I write articles for many different online publications, and manage my own blog where I share my thoughts on a variety of topics.

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