Trigonometrical Ratios of 90 Degree Minus Theta | Relation between Quadrants | Solved Examples

Are you looking for any material to know the relation between all Trigonometrical Ratios of 90 Degree Minus Theta? Then, you can relax now. On this page, we have enclosed the detailed information on the relation between Trigonometric Ratios of (90Â° – Î¸) along with the proofs. Get the example questions and step-by-step solutions in the following sections of this article. Check out the simple formula to memorize the Trigonometric Functions.

How to Determine the Trigonometric Ratios of 90 Degree Minus Theta?

Here, you can see Trigonometrical Functions of 90 Degree Minus Theta can be determined. As per the ASTC “All Silver Tea Cups” or “All Students Take Calculus”

A means All, S means “SinÎ¸, CosecÎ¸”, T means “TanÎ¸, CotÎ¸”, C means CosÎ¸, SecÎ¸.

The pictorial representation of the ASTC formula is as follows:

From the above picture, (90Â° – Î¸) falls in the first quadrant.

sin (90Â° â€“ Î¸) = cos Î¸

cos (90Â° â€“ Î¸) = sin Î¸

tan (90Â° â€“ Î¸) = cot Î¸

cosec (90Â° â€“ Î¸) = sec Î¸

sec (90Â° â€“ Î¸) = cosec Î¸

cot (90Â° â€“ Î¸) = tan Î¸

Evaluate Trigonometrical Ratios of 90 Degree Minus Theta

1. Evaluate Sin(90Â° â€“ Î¸)?

To evaluate sin (90Â° – Î¸), we have to consider the following important points.

• Â (90Â° – Î¸) will fall in the 1st quadrant.
• Â When we have 90Â°, “sin” will become “cos”.
• Â In the 1st quadrant, the sign of “sin” is positive.

Considering the above points, we have

Sin (90Â° – Î¸) = Cos Î¸

2. Evaluate Cos(90Â° â€“ Î¸)?

To evaluate cos (90Â° – Î¸), we have to consider the following important points.

• (90Â° – Î¸) will fall in the 1st quadrant.
• Â When we have 90Â°, “cos” will become “sin”.
• Â In the 1st quadrant, the sign of “cos” is positive.

Considering the above points, we have

Cos (90Â° – Î¸) = Sin Î¸

3. Evaluate Tan(90Â° â€“ Î¸)?

To evaluate tan (90Â° – Î¸), we have to consider the following important points.

• Â (90Â° – Î¸) will fall in the 1st quadrant.
• Â When we have 90Â°, “tan” will become “cot”.
• Â In the 1st quadrant, the sign of “tan” is positive.

Considering the above points, we have

Tan (90Â° – Î¸) = Cot Î¸

4. Evaluate Cot(90Â° â€“ Î¸)?

To evaluate cot (90Â° – Î¸), we have to consider the following important points.

• Â (90Â° – Î¸) will fall in the 1st quadrant.
• Â When we have 90Â°, “cot” will become “tan”
• Â In the 1st quadrant, the sign of “cot” is positive.

Considering the above points, we have

Cot (90Â° – Î¸) = Tan Î¸

5. Evaluate Cosec(90Â° â€“ Î¸)?

To evaluate Cosec (90Â° – Î¸), we have to consider the following important points.

• (90Â° – Î¸) will fall in the 1st quadrant.
• Â When we have 90Â°, “Cosec” will become “sec”.
• Â In the 1st quadrant, the sign of “Cosec” is positive.

Considering the above points, we have

Cosec (90Â° – Î¸) = Sec Î¸

6. Evaluate Sec(90Â° â€“ Î¸)?

To evaluate sec (90Â° – Î¸), we have to consider the following important points.

• Â (90Â° – Î¸) will fall in the 1st quadrant.
• Â When we have 90Â°, “sec” will become “cosec”.
• Â In the 1st quadrant, the sign of “sec” is positive.

Considering the above points, we have

Sec (90Â° – Î¸) = Cosec Î¸

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Solved Examples on Trigonometric Ratios of 90Â° – Î¸

Example 1:

Find the value of Tan 45Â°?

Solution:

Tan 45Â° = Tan (90Â° – 45Â°)

We know that Tan (90Â° – Î¸) = Cot Î¸

So, Tan 45Â° = Cot 45Â°

= 1Â  [Cot 45Â° = 1]

Therefore, Tan 45Â° = 1.

Example 2:

Find the value of Sin 65Â°?

Solution:

Sin 65Â° = Sin (90Â° – 25Â°)

We know that Sin (90Â° – Î¸) = Cos Î¸

So, Sin 65Â° = Cos 25Â°

= 0.906308 [ Cos 25Â° = 0.906308]

Therefore, Sin 65Â° = 0.906308

Example 3:

Find the value of Cot 80Â°?

Solution:

Cot 80Â° = Cot (90Â° – 10Â°)

We know that Cot (90Â° – Î¸) = Tan Î¸

So, Cot 80Â° = Tan 10Â°

= 0.17633 [ Tan 10Â° = 0.17633]

Therefore, Cot 80Â° = 0.17633

Example 4:

Find the value of Cos 50Â°?

Solution:

Cos 50Â° = Cos (90Â° – 40Â°)

We know that Cos (90Â° – Î¸) = Sin Î¸

So, Cos 50Â° = Sin(40Â°)

= 0.64278760968 [ Sin(40Â°) = 0.64278760968]

Therefore, Cos 50Â° = 0.64278760968.

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