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PCSL
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How do you do stuff like sin(pi/4) in your head or sin(1) or sec(pi(x))? Thanks for your help. I'm in Calc II and fully understand the calculus but my trig foundation from high school isn't the best.
There are a small angles whose sines and cosines you should have memorized:PCSL said:How do you do stuff like sin(pi/4) in your head or sin(1) or sec(pi(x))? Thanks for your help. I'm in Calc II and fully understand the calculus but my trig foundation from high school isn't the best.
Mark44 said:Do you mean, formulas such as sin(2x) = 2sin(x)cos(x) and the like? If so, these are worth memorizing, IMO.
To evaluate trig identities without a calculator, you need to know the basic trigonometric identities, such as the Pythagorean identities, double angle identities, and sum and difference identities. Then, you can use algebraic manipulation, substitution, and other mathematical techniques to simplify the expression and evaluate it.
The most common trig identities used for evaluating expressions without a calculator are the Pythagorean identities (sin²x + cos²x = 1, tan²x + 1 = sec²x, cot²x + 1 = csc²x), double angle identities (sin2x = 2sinx cosx, cos2x = cos²x - sin²x, tan2x = 2tanx / 1 - tan²x), and sum and difference identities (sin(x ± y) = sinx cosy ± cosx siny, cos(x ± y) = cosx cosy ∓ sinx siny).
No, not all expressions can be evaluated using trig identities without a calculator. Some expressions may require advanced techniques or may not have a simplified form. It is important to have a good understanding of trigonometric identities and when they can be used to evaluate an expression.
You can check your answer by using a calculator or by verifying your steps and simplification process. You can also use online resources or ask a colleague or teacher to check your work.
Some tips for simplifying and evaluating trig identities without a calculator include using the most appropriate identity for the given expression, factoring and canceling terms, using the unit circle to convert between trigonometric functions, and practicing regularly to improve your skills.