Cos 90 Degrees: Table, Fraction, Unit Circle

What is the Value of Cos 90 Degrees: The sine function, cosine function, and tangent function are the three most well-known trigonometric ratios in trigonometric functions. It is commonly specified for angles smaller than a right angle. Trigonometric functions are written as the ratio of two sides of a right triangle containing the angle, the values of which may be found in the length of various line segments around a unit circle. Degrees are often represented as 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360°. The first quadrant is considered to be located between 0 degrees and 90 degrees. The third quadrant has angles between 180 degrees and 270 degrees, whereas the second quadrant contains angles ranging between 90 degrees and 180 degrees. The fourth quadrant covers the range of 270 degrees to 360 degrees.

In the fourth quadrant, Cos stays positive. It is important to note that everything in the first one is positive. Tan is also positive in the second and third quadrant. For example, the distance from a point to the origin stays positive, but the X and Y coordinates might be either negative or positive. Thus, in the first quadrant, all coordinates are positive, but in the second quadrant, only sine and cosecant are positive. Tangent and cotangent are only positive in the third quadrant, but cosine and secant stay positive in the fourth. Let us now look at the value for cos 90 degrees, which is equal to zero, and how the values are calculated using the quadrants of a unit circle.

Cos 90 Degrees or Cos 90º

Now that we have already provided you with the value of Cosine 90, let us help you in finding out how this value is calculated. For this, we will require a right-angled triangle.

In the above figure, we have a right-angle triangle PQR, right-angled at Q. ‘a’ is the perpendicular, ‘b’ is the base and ‘h’ is the hypotenuse.

And the formula for Cosθ = \(\frac{Base}{Hypotenuse}\) = \(\frac{b}{h}\).

So, using the above, we can calculate the values of various cosine angles.

• Cos 0° = \(\sqrt{\frac{0}{4}}\)  = 1
• Cos 30° = \(\sqrt{\frac{1}{4}}\)  = √3/2
• Cos 45° = \(\sqrt{\frac{2}{4}}\)  = 1/√ 2
• Cos 60° = \(\sqrt{\frac{3}{4}}\)  = ½
• Cos 90° = \(\sqrt{\frac{4}{4}}\)  = 0

What is COS 90 in Radians & Degrees?

You can check the values from the table below:

Cosine Trigonometric Ratios Table

The values for Cos and Sin can be derived from each other as:

• Sin 0 = Cos 90
• Sin 30 = Cos 60
• Sin 45 = Cos 45
• Sin 60 = Cos 30
• Sin 90 = Cos 0 and so on.

And using the values of Cos and Sin, you can find the value of Tan as:

Tanθ = \(\frac{Sin θ}{Cos θ}\)

From the table below, you can check the values for Sin, Cos, Tan at different angles:

Trigonometric Ratios Table

Now that we have helped you in figuring out the process to find Cos, Sin, Tan values, you can use the above method to complete the trigonometric table. Using the values of Sine, Cosine, and Tangent, you can find Cosec, Sec, and Cot values.

• a) Cosec = 1/Sin
• b) Sec = 1/Cos
• c) Cot = 1/Tan or Cos/Sin

Trigonometric Formulas

Here are some formulas that will aid you in your preparation.

• (i) Sin (A + B) = Sin A Cos B + Cos A Sin B
• (ii) Sin (A – B) = Sin A Cos B – Cos A Sin B
• (iii) Cos (A + B) = Cos A Cos B – Sin A Sin B
• (iv) Cos (A – B) = Cos A Cos B + Sin A Sin B
• (v) Sin 2A = 2 Sin A Cos A
• (vi) Cos 2A = Cos² A – Sin² A = 1 – 2 Sin² A = 2 Cos² A – 1
• (vii) Cos 3A = 4Cos³ A – 3Cos A
• (viii) 2Sin A Cos B = Sin (A + B) + Sin (A – B)
• (ix) 2Cos A Sin B = Sin (A + B) – Sin (A – B)
• (x) 2Cos A Cos B = Cos (A + B) + Cos (A – B)
• (xi) 2Sin A Sin B = Cos (A – B) – Cos (A + B)

Study on Embibe

Students can access the following study materials on Embibe for their exam preparation:

FAQs on Value of Cos 90 Degree

Q. What is the value of cos 90 degrees?
Ans. Cos 90 has 0 (zero) value, which is equivalent to Sin 0.

Q. How to find the value of cos 90?
Ans. One way to find Cos 90 is to find Sin 0 as Sin 0 = Cos 90. The value of both is 0.
You can also use the right-angled triangle method in which Cos = Base/Hypotenuse.

Q. What is the value of Cos 90 degrees in relation to Sin 90 degrees?
Ans. We may express cos 90° in terms of sin 90° using trigonometric identities as cos(90°) = √(1 – sin²(90°)). In this case, sin 90° equals one.

Q. What is the Cos 90° value in terms of Cosec 90°?
Ans. Since the cosecant function may be used to represent the cosine function, we can write cos 90° as  [√(cosec²(90°) – 1)/cosec 90°]. The value of cosec 90° is one.

Q. Find the value of cos 135°?
Ans. Cos 135° can be written as Cos(90° + 45°)
Using the formula, Cos(a+b) = Cos a Cos b – Sin a Sin b
So, Cos 135° = Cos 90° Cos 45° – Sin 90° Sin 45°
cos 135° = 0 x 1/√2 – 1 x 1/√2
cos 135° = – 1/√2.