# T-Ratios of Related Angles

### T-Ratios of (90° − θ)

sin (90° − θ) = cos θ

cos (90° − θ) = sin θ

tan (90° − θ) = = cot θ

cosec (90° − θ) = sec θ

sec (90° − θ) = cosec θ

cot (90° − θ) = tan θ

### T-Ratios of (90° + θ)

sin (90° + θ) = cos θ

cos (90° + θ) = −sin θ

tan (90° + θ) = −cot θ

cosec (90° + θ) = sec θ

sec (90° + θ) = −cosec θ

cot (90° + θ) = −tan θ

### T-Ratios of (180° − θ)

sin (180° − θ) = sin θ

cos (180° − θ) = −cos θ

tan (180° − θ) = −tan θ

cosec (180° − θ) = cosec θ

sec (180° − θ) = −sec θ

cot (180° − θ) = −cot θ

### T-Ratios of (180° + θ)

sin (180° + θ) = −sin θ

cos (180° + θ) = −cos θ

tan (180° + θ) = tan θ

cosec (180° + θ) = −cosec θ

sec (180° + θ) = −sec θ

cot (180° + θ) = cot θ

Since 360° corresponds to one full revolution, sine of the angles 360°+45°; 720°+45°; 1080°+45° are equal to sine of 45°. This is so for the other trigonometric ratios. When an angle exceeds 360°, it can be reduced to an angle between 0° and 360° by wiping out integral multiples of 360°.