Basicly, i am bad at mathematics very hard to me got score 70. I try learn trigonometry now, starting from the very basic.
I practice to find the value of $$\sin(135^\circ)$$ using my knowing about $\sin(45^\circ)={\sqrt2\over2}$, $\cos(45^\circ)={\sqrt2 \over 2}$, $\sin(90^\circ)=1$, $\cos(90^\circ)=0$, the quadrant rule and sum angle formula. I hope the expert can help me to correcting and giving a tips.
Using the quadrant rule :
Since $135^\circ$ on second quadrant the sine sign is positive
Using sum formula of sin :
$$\sin(135^\circ)=\sin(90^\circ+45^\circ)$$
$$=\sin(90^\circ)×\cos(45^\circ)+\cos(90^\circ)×\sin(45^\circ)$$
$$=1×\cos(45^\circ)+0×\sin(45^\circ)$$
$$=\cos(45^\circ)+0$$
$$=\cos(45^\circ)$$
$$={\sqrt2\over2}$$
For your informatiom, i am just economic faculty at second semester, and my college tutor giving us a calculus, that contain trigonometry. I need to learn this because 2 weeks again i got calculus examination. Thank you for your support and tips and explanation.
Is my practice is correct ? Can i get the simple way to remember the sum formula of sine and cosine ? What suitable practice for me after i practicing with $135^\circ$ ?
Best Answer
You don't need in that case use these formula, indeed by the definition of trigonometric function by the unit circle and by symmetry we can directly conclude that:
$$\sin(135^\circ)=\sin(90^\circ+45^\circ)=\sin 45°$$
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