What is exact value of tan 45?

Tan 45 is the value of the tangent function of 45 degrees. The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

In a right triangle with a 45-degree angle, the opposite and adjacent sides are equal in length. Thus, the value of the tangent function can be calculated by dividing the length of the opposite side by the length of the adjacent side.

Since the opposite and adjacent sides are equal in length in a 45-degree angle, the value of the tangent function of 45 degrees is 1. This means that the length of the opposite side is equal to the length of the adjacent side.

Therefore, the exact value of tan 45 is 1.

What is the value of tan if the angle is 45?

What is the value of tan if the angle is 45? This is a common question in trigonometry and it is important to know the answer. When the angle is 45 degrees, the value of the tangent function, tan, can be calculated. In trigonometry, tan represents the ratio of the length of the opposite side to the length of the adjacent side.

The value of tan(45) can be determined by using the special values of the tangent function for certain angles. One of these special values is for the angle of 45 degrees. This angle is special because the length of the opposite side is equal to the length of the adjacent side in a right triangle.

With a right triangle, the opposite side is the side that is opposite to the angle of interest, and the adjacent side is the side that is next to the angle of interest. In the case of a 45-degree angle, both the opposite side and the adjacent side have the same length. Therefore, the ratio of the opposite side to the adjacent side is 1.

So, tan(45) = 1. This means that when the angle is 45 degrees, the value of the tangent function is 1. This value is useful in many calculations and applications, such as in finding the slope of a line or in solving trigonometric equations.

In conclusion, when the angle is 45 degrees, the value of the tangent function (tan) is 1. This value is important in trigonometry and has various applications in mathematics and other fields.

Why is tan 45 )= 1?

Tan 45 is equal to 1 because of the special properties of the trigonometric function tangent. Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In a right triangle with an angle of 45 degrees, the opposite and adjacent sides are equal in length.

By using the Pythagorean theorem, we can calculate the length of the sides in a right triangle with a 45-degree angle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

For a 45-degree angle, the two shorter sides are of equal length. Let's call this length "x". By applying the Pythagorean theorem, we get x^2 + x^2 = hypotenuse^2. Simplifying this equation, we obtain 2x^2 = hypotenuse^2. Taking the square root of both sides, we find that x = hypotenuse/sqrt(2).

Since the tangent of an angle is equal to the ratio of the opposite side to the adjacent side, in this case, tan 45 = x/x = 1. Therefore, tan 45 is equal to 1.

This property of the tangent function is important in applications such as navigation, physics, and engineering, where angles and ratios are frequently used to solve problems and make calculations.

What is tan 45 without calculator?

Tan is a trigonometric function that represents the ratio of the sine of an angle to the cosine of the same angle. In simpler terms, it's the measure of the opposite side over the adjacent side in a right triangle.

The value of tan 45 can be calculated without a calculator using the properties of right triangles. This can be done by knowing that in a right triangle, the angles measure 45 degrees, 45 degrees, and 90 degrees. Since we know that the opposite and adjacent sides are the same length in a 45-45-90 triangle, we can rely on this property to find the value of tan 45.

Using the Pythagorean theorem, we can determine that the hypotenuse (the side opposite the right angle) of a 45-45-90 triangle is equal to the square root of 2 times the length of one of the legs. So, if we consider the length of each leg as 1, then the hypotenuse would be √2.

To find the value of tan 45, we need to divide the length of the side opposite the angle (which is 1) by the length of the adjacent side (which is also 1). Thus, tan 45 = 1/1 = 1.

Therefore, without a calculator, we can determine that the value of tan 45 is equal to 1.

Which of the following is the correct value of tan 45?

Tan 45 is equal to 1. In trigonometry, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. When we have a right triangle with an angle of 45 degrees, the opposite side and the adjacent side are equal in length. Therefore, the ratio is 1.

It is important to remember that the value of tan 45 is a special value in trigonometry. Since it is equal to 1, it means that the opposite side and the adjacent side have the same length in a right triangle with a 45-degree angle. This is useful in various mathematical and engineering applications.

The value of tan 45 can also be expressed as a decimal. When we calculate it, the result is approximately 0.9999999999999999. However, in practical applications, we often round it to 1 for simplicity.

In conclusion, the correct value of tan 45 is 1. This value represents the ratio of the length of the opposite side to the length of the adjacent side in a right triangle with a 45-degree angle. It is a special value in trigonometry and is commonly used in various fields of mathematics and engineering.