Mathematics for Mechanical Engineers.pptx

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1. Mathematics for Mechanical Engineers

2. Trigonometric functions 𝑠𝑖𝑛𝑥, 𝑐𝑜𝑠𝑥, 𝑡𝑎𝑛𝑥, 𝑐𝑜 𝑠𝑒𝑐𝑥, 𝑠𝑒𝑐𝑥, 𝑎𝑛𝑑 𝑐𝑜𝑡𝑥 Inverse trigonometric functions 𝑠𝑖𝑛−1𝑥, 𝑐𝑜𝑠−1𝑥, 𝑡𝑎𝑛−1𝑥, 𝑐𝑜𝑠𝑒𝑐−1𝑥, 𝑠𝑒𝑐−1𝑥, 𝑎𝑛𝑑 𝑐𝑜𝑡−1𝑥

3. Trigonometric functions of complementary angles (𝟗𝟎° − 𝒙) sin(90°−𝑥) = cos𝑥 cos(90°−𝑥) = sin𝑥 tan(90°−𝑥) = cot𝑥 cosec(90°−𝑥) = sec𝑥 sec(90°−𝑥) = cosec𝑥 cot(90°−𝑥) = tan𝑥

4. Trigonometric functions of negative angles sin(−𝑥) = −sin𝑥 cos(−𝑥) =cos𝑥 tan(−𝑥) = −tan𝑥 cosec(−𝑥) = −cosec𝑥 sec(−𝑥) = sec𝑥 cot(−𝑥) = −cot𝑥