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You use the definitions of secant (sec) and cosecant (csc):
sec x = 1/cos x
csc x = 1/sin x
→ sec² 45° + csc² 60°
= (1/cos 45°)² + 1/(sin 60°)²
= (1/(1/√2))² + (1/(√3/2))²
= (√2)² + (2/√3)²
= 2 + 4/3
= 10/3 = 3⅓
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In a right-triangle with an angle of 45°, the other angle is 45° and the sides are in the ratio of 1 : 1 : √2
(sides opposite angles 45° : 45° : 90°) giving cos 45° = 1/√2
In a right triangle with an angle of 60°, the other angle is 30° and the sides are in the ratio of √3 : 1 : 2 (sides opposite angles 60° : 30° : 90°) giving sin 60° = √3/2
These ratios can be confirmed/calculated by Pythagoras; in the first case it is an isosceles triangle with legs of length 1 unit, and in the second case it is half an equilateral triangle (one angle bisected by a perpendicular from the opposite side) with side length 2 units.
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What is tan x csc x?
tan(x)*csc(x) = sec(x)
How do you put sec in a TI 84 calculator?
For any calculator Sec(Secant) = 1/Cos Csc (Cosecant) = 1/ Sin Cot (Cotangent) = 1/Tan
What does 32 min 9 sec plus 40 min 10 sec equals?
32 min 9 sec 40 min 10 sec adding gives... 71 min 19 sec 1 hr 11 min 19 sec. ■
What is sec squared theta minus tan squared theta?
1 - sin2(q) = cos2(q)dividing through by cos2(q),sec2(q) - tan2(q) = 1
What is the derivative of tangent?
the derivative of tangent dy/dx [ tan(u) ]= [sec^(2)u]u' this means that the derivative of tangent of u is secant squared u times the derivative of u.
What is sec squared x times csc x divided by sec squared x plus csc squared x?
Ah, secant, annoying as always. Why don't we use its definition as 1/cos x and csc as 1/sin x? We will do that Also, please write down the equation, there is at least TWO different equations you are talking about. x^n means x to the power of n 1/(sin x) ^2 is csc squared x, it's actually csc x all squared 1/(cos x) ^2 in the same manner.
Csc divided by cot squared equals tan multiplied by sec?
Yes.
How are the graphs of sec x and csc x related?
They are co-functions meaning that 90 - sec x = csc x.
What is tan x csc x?
tan(x)*csc(x) = sec(x)
Csc squared divided by cot equals csc x sec. can someone make them equal?
cot(x)=1/tan(x)=1/(sin(x)/cos(x))=cos(x)/sin(x) csc(x)=1/sin(x) sec(x)=1/cos(x) Therefore, (csc(x))2/cot(x)=(1/(sin(x))2)/cot(x)=(1/(sin(x))2)/(cos(x)/sin(x))=(1/(sin(x))2)(sin(x)/cos(x))=(1/sin(x))*(1/cos(x))=csc(x)*sec(x)
What is sin cos tan csc sec cot of 135 degrees?
All those can be calculated quickly with your calculator. Just be sure it is in "degrees" mode (not in radians). Also, use the following identities: csc(x) = 1 / sin(x) sec(x) = 1 / cos(x) cot(x) = 1 / tan(x) or the equivalent cos(x) / sin(x)
Sec squared theta plus tan squared theta equals to 13 12 and sec raised to 4 theta minus tan raised to 4 theta equals to how much?
It also equals 13 12.
What is the second derivative of ln(tan(x))?
f'(x) = 1/tan(x) * sec^2(x) where * means multiply and ^ means to the power of. = cot(x) * sec^2(x) f''(x) = f'(cot(x)*sec^2(x) + cot(x)*f'[sec^2(x)] = -csc^2(x)*sec^2(x) + cot(x)*2tan(x)sec^2(x) = sec^2(x) [cot(x)-csc^2(x)] +2tan(x)cot(x) = sec^2(x) [cot(x)-csc^2(x)] +2
How do i simplify csc theta divided by sec theta?
By converting cosecants and secants to the equivalent sine and cosine functions. For example, csc theta is the same as 1 / sin thetha.
What is six trigonometric ratios of 45 degrees?
sin(45) = cos(45) = 1/sqrt(2) tan(45) = cot(45)= 1 csc(45) = sec(45) = sqrt(2)
What is sin cos tan csc sec cot of 30 45 60 degrees?
Sin(30) = 1/2 Sin(45) = root(2)/2 Sin(60) = root(3)/2 Cos(30) = root(3)/2 Cos(45) = root(2)/2 Cos(60) = 1/2 Tan(30) = root(3)/3 Tan(45) = 1 Tan(60) = root(3) Csc(30) = 2 Csc(45) = root(2) Csc(60) = 2root(3)/3 Sec(30) = 2root(3)/3 Sec(45) = root(2) Sec(60) = 2 Cot(30) = root(3) Cot(45) = 1 Cot(60) = root(3)/3
How do you put sec in a TI 84 calculator?
For any calculator Sec(Secant) = 1/Cos Csc (Cosecant) = 1/ Sin Cot (Cotangent) = 1/Tan
