All Sin Tan Cos Rule

What is all sin tan cos rule?

All sin tan cos rule is all trigonometrical ratios in the first quadrant, only sin (and cosec) in the second quadrant, only tan (and cot) in the third quadrant and only cos (and sec) in the fourth quadrant are positive.

We know the signs of trigonometrical ratios are:

(i) When the θ lies in the first quadrant:  All trigonometrical ratios of the angle θ are positive.

(ii) When the θ lies in the second quadrant: Only sin θ, csc θ are positive and the rest are negative.

(iii) When the θ lies in the third quadrant: Only tan θ and cot θ are positive and the rest are negative

(iv) When the θ lies in the fourth quadrant: Only cos θ and sec θ are positive and the rest are negative.

Therefore, the above rule for the signs of trigonometrical ratios is also known “all, sin, tan, cos” rule.

Note:

1. The relations of all the trigonometrical ratios of a positive acute angle and angle θ can either be positive or negative.

2. The values of sin θ cannot be greater than 1 i.e., -1 ≤ sin θ ≤ 1

3. The values of cos θ cannot be greater than 1 i.e., -1 ≤ cos θ ≤ 1

4. The values of sec θ cannot be less than 1 i.e., sec Ѳ ≥ 1 or sec θ ≤ -1

5. The values of csc θ cannot be less than 1 i.e., csc θ ≥ 1 or csc θ ≤ -1

6. Tan θ and cot θ can have any real values.

● Trigonometric Functions

• Basic Trigonometric Ratios and Their Names
• Restrictions of Trigonometrical Ratios
• Reciprocal Relations of Trigonometric Ratios
• Quotient Relations of Trigonometric Ratios
  
• Limit of Trigonometric Ratios
  
• Trigonometrical Identity
• Problems on Trigonometric Identities
• Elimination of Trigonometric Ratios
• Eliminate Theta between the equations
• Problems on Eliminate Theta
• Trig Ratio Problems
• Proving Trigonometric Ratios
• Trig Ratios Proving Problems
• Verify Trigonometric Identities
• Trigonometrical Ratios of 0°
• Trigonometrical Ratios of 30°
• Trigonometrical Ratios of 45°
• Trigonometrical Ratios of 60°
• Trigonometrical Ratios of 90°
• Trigonometrical Ratios Table
• Problems on Trigonometric Ratio of Standard Angle
  
• Trigonometrical Ratios of Complementary Angles
• Rules of Trigonometric Signs
• Signs of Trigonometrical Ratios
  
• All Sin Tan Cos Rule
• Trigonometrical Ratios of (- θ)
• Trigonometrical Ratios of (90° + θ)
• Trigonometrical Ratios of (90° - θ)
• Trigonometrical Ratios of (180° + θ)
• Trigonometrical Ratios of (180° - θ)
• Trigonometrical Ratios of (270° + θ)
• Trigonometrical Ratios of (270° - θ)
• Trigonometrical Ratios of (360° + θ)
• Trigonometrical Ratios of (360° - θ)
• Trigonometrical Ratios of any Angle
• Trigonometrical Ratios of some Particular Angles
• Trigonometric Ratios of an Angle
• Trigonometric Functions of any Angles
• Problems on Trigonometric Ratios of an Angle
• Problems on Signs of Trigonometrical Ratios

11 and 12 Grade Math

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