Results of Trigonometric Ratios of Allied Angles
$$\alpha $$
|
$$Sin\alpha $$
|
$$Cos\alpha $$
|
$$Tan\alpha $$
|
$$Cot\alpha $$
|
$$Sec\alpha $$
|
$$Co\sec \alpha $$
|
$$ – \theta $$
|
$$ – Sin\theta $$
|
$$ + Cos\theta $$
|
$$ – Tan\theta $$
|
$$ – Cot\theta $$
|
$$ + Sec\theta $$
|
$$ – Co\sec \theta $$
|
$${90^ \circ } – \theta $$
|
$$ + Cos\theta $$
|
$$ + Sin\theta $$
|
$$ + Cot\theta $$
|
$$ + Tan\theta $$
|
$$ + Co\sec \theta $$
|
$$ + Sec\theta $$
|
$${90^ \circ } + \theta $$
|
$$ + Cos\theta $$
|
$$ – Sin\theta $$
|
$$ – Cot\theta $$
|
$$ – Tan\theta $$
|
$$ – Co\sec \theta $$
|
$$ + Sec\theta $$
|
$${180^ \circ } – \theta $$
|
$$ + Sin\theta $$
|
$$ – Cos\theta $$
|
$$ – Tan\theta $$
|
$$ – Cot\theta $$
|
$$ – Sec\theta $$
|
$$ + Co\sec \theta $$
|
$${180^ \circ } + \theta $$
|
$$ – Sin\theta $$
|
$$ – Cos\theta $$
|
$$ + Tan\theta $$
|
$$ + Cot\theta $$
|
$$ – Sec\theta $$
|
$$ – Co\sec \theta $$
|
$${270^ \circ } – \theta $$
|
$$ – Cos\theta $$
|
$$ – Sin\theta $$
|
$$ + Cot\theta $$
|
$$ + Tan\theta $$
|
$$ – Co\sec \theta $$
|
$$ – Sec\theta $$
|
$${270^ \circ } + \theta $$
|
$$ – Cos\theta $$
|
$$ + Sin\theta $$
|
$$ – Cot\theta $$
|
$$ – Tan\theta $$
|
$$ + Co\sec \theta $$
|
$$ – Sec\theta $$
|
$${360^ \circ } – \theta $$
|
$$ – Sin\theta $$
|
$$ + Cos\theta $$
|
$$ – Tan\theta $$
|
$$ – Cot\theta $$
|
$$ + Sec\theta $$
|
$$ – Co\sec \theta $$
|
$${360^ \circ } + \theta $$
|
$$ + Sin\theta $$
|
$$ + Cos\theta $$
|
$$ + Tan\theta $$
|
$$ + Cot\theta $$
|
$$ + Sec\theta $$
|
$$ + Co\sec \theta $$
|
1. $$Sin( – \theta ) = – Sin\theta $$
2. $$Cos( – \theta ) = Cos\theta $$
3. $$Tan( – \theta ) = – Tan\theta $$
4. $$Sin({90^ \circ } – \theta ) = Cos\theta $$
5. $$Cos({90^ \circ } – \theta ) = Sin\theta $$
6. $$Tan({90^ \circ } – \theta ) = Cot\theta $$
7. $$Sin({180^ \circ } – \theta ) = Sin\theta $$
8. $$Cos({180^ \circ } – \theta ) = – Cos\theta $$
9. $$Tan({180^ \circ } – \theta ) = – Tan\theta $$
10. $$Sin({270^ \circ } – \theta ) = – Cos\theta $$
11. $$Cos({270^ \circ } – \theta ) = – Sin\theta $$
12. $$Tan({270^ \circ } – \theta ) = Cot\theta $$
13. $$Sin({90^ \circ } + \theta ) = Cos\theta $$
14. $$Cos({90^ \circ } + \theta ) = – Sin\theta $$
15. $$Tan({90^ \circ } + \theta ) = – Cot\theta $$
16. $$Sin({180^ \circ } + \theta ) = – Sin\theta $$
17. $$Cos({180^ \circ } + \theta ) = – Cos\theta $$
18. $$Tan({180^ \circ } + \theta ) = Tan\theta $$
19. $$Sin({270^ \circ } + \theta ) = – Cos\theta $$
20. $$Cos({270^ \circ } + \theta ) = Sin\theta $$
21. $$Tan({270^ \circ } + \theta ) = – Cot\theta $$
22. The period of $$Sin\theta $$ and $$Cos\theta $$ is $$2\pi $$, whereas the period of $$Tan\theta $$ and $$Cot\theta $$ is $$\pi $$.
If $$k$$ is any integer, then
23. $$Sin(k\pi ) = 0$$
24. $$Cos(k\pi ) = {( – 1)^k}$$
25. $$Sin(k\pi + \beta ) = {( – 1)^k}Sin\beta $$
26. $$Cos(k\pi + \beta ) = {( – 1)^k}Cos\beta $$
27. $$Sin\left[ {(2k + 1)\frac{\pi }{2} + \beta } \right] = {( – 1)^k}Cos\beta $$
28. $$Cos\left[ {(2k + 1)\frac{\pi }{2} + \beta } \right] = {( – 1)^{k + 1}}Sin\beta $$
Yash Sharma
June 22 @ 11:22 am
Why cos 90+A = – Sin A?