Trigonometry Help? Find the exact value of each expression. if undefined, write undefined.?
sin 315° = sin(360°-45°) = -sin(45°) = -1/√2 tan(-5π/4) = - tan(5π/4) = - tan(π + π/4) = - tan(π/4) = -1 cot(510°) = cot(360°+180°-30°) = cot(180°-30°) = - cot(30°) = √3 sec(3π/2) = sec(π+π/2) = -sec(π/2) = -∞ cosec(17π/6) = cosec(2π+π-π/6) = cosec(π-π/6) = cosec(π/6) = 2
Trigonometry help, find exact value of tan(22.5degrees)?
Sometimes I forget half-angle formulas, so I use a double-angle formula instead. 2tan(22.5°)/[1 - tan²(22.5°)] = tan[2(22.5°)] 2tan(22.5°)/[1 - tan²(22.5°)] = tan(45°) 2tan(22.5°)/[1 - tan²(22.5°)] = 1 2tan(22.5°) = 1 - tan²(22.5°) tan²(22.5°) + 2tan(22.5°) - 1 = 0 Apply the quadratic formula. tan(22.5°) = -1 ± √(2) It is in quadrant I, so reject the negative solution. tan(22.5°) = √(2) - 1
Trigonometry Help? Find the exact value of the expression. if undefined, write undefined?
1. 0; 180 degrees is on the x-axis, sin a represents a y-value, all y-values on x-axis are zero 2. -sqrt3 3. secant = 1/cosine; cos450 = cos90 = 0; sec450 = Undefined 4. cos(-19pi/6) = cos(-7pi/6) = cos(7pi/6) = (sqrt3) / 2 Use your calculator in radian mode
What does "exact value" mean in trigonometry?
It means if the answer is sqrt(3), then write the answer as sqrt(3) and not 1.73. cos(30) = sqrt(3)/2 Your calculator may give you cos(30) = 0.866025403784 The exact value is sqrt(3)/2 The approximate value is 0.866025403784
[TRIG HELP] Exact Value of Expressions?
The easiest way would be to remember the pythagorean identities: csc(t)^2 - cot(t)^2 = 1 sec(t)^2 - tan(t)^2 = 1 sin(t)^2 + cos(t)^2 = 1 cot(arcsin(5/13)) => cos(arcsin(5/13)) / sin(arcsin(5/13)) => sqrt(cos(arcsin(5/13))^2) / (5/13) => (13/5) * sqrt(1 - sin(arcsin(5/13))^2) => (13/5) * sqrt(1 - (5/13)^2) => (13/5) * sqrt(169/169 - 25/169) => (13/5) * sqrt(144/169) => (13/5) * (+/- 12/13) => +/- 12/5 cos(arcsin(-4/5)) => sqrt(1 - sin(arcsin(-4/5))^2) => sqrt(1 - 16/25) => sqrt(9/25) => +/- 3/5 tan(arccos(-1/4)) => sin(arccos(-1/4)) / cos(arccos(-1/4)) => sqrt(1 - (-1/4)^2) / (-1/4) => -4 * sqrt(15/16) => -4 * (+/- 1/4) * sqrt(15) => +/- sqrt(15) sec(arcsin(-sqrt(2)/2)) => 1/cos(arcsin(-sqrt(2)/2)) => 1/sqrt(1 - (-sqrt(2)/2)^2) => 1/sqrt(1 - 2/4) => 1/sqrt(2/4) => sqrt(4/2) => sqrt(2)
Pre-calc (Trigonometry) Help?
Hi, From looking at the graph, I get: y = 4sin(3x) - 7cos(3x) is the same as y = √(65)sin(3(x - 20.08503957°)) <==ANSWER √(4² + 7²) = √65 for the amplitude The first x intercept as the value of "h" is where 4sin(3x) - 7cos(3x) = 0. This means that "h" occurs where 4sin(3x) = 7cos(3x) Dividing by 4cos(3x) gives 4sin(3x).....7cos(3x) -----------.=.------------- 4cos(3x)....4cos(3x) sin(3x)......7 -----------.=.--- cos(3x).....4 7 -- = tan(3x) 4 3x = tan^(-1) (7/4) = 60.2551187 3x = 60.2551187 x = 20.08503957 <==This is the value of "h". If you want to be REALLY exact, then write your equation as: y = √(65)sin(3(x - ⅓tan^(-1) (7/4))) <==MEGA-EXACT ANSWER I hope that helps!! :-)
What does exact value mean in trig?
It means don't use your calculator, find an exact mathematical expression. For example, sin 60 is not 0.866, it's sqrt(3)/2 (exactly).
How do I find the exact value of this sum or difference trigonometry problem: sin (7pi/30) cos (pi/15)-cos (7pi/30) sin (pi/15)?
Does the formula sin(A – B) = sin(A)cos(B) = cos(A)sin(B) look familiar?If it does, it should be obvious that we can let A = 7π/30 and B = π/30so the answer is sin(7π/30 – π/30) = sin(5π/30) = sin(π/6) = ½
How to find the exact functions of trig values! PLEASE HELP?
You can ONLY find the exact values without a calculator s^2 + c^2 = 1 for 45° 2 sin^2 45° = 1 sin^2 45°= 1/2 Sin 45° = (1/2)^(1/2) = Cos 45° Cos 60° = 1/2 Sin 60° = 3^(1/2)/2 csc 45° = 1/Sin 45° = 2^(1/2) Tan 60° = Sin 60°/Cos 60° = 3^(1/2)/ Sin 90° = 1 Tan 180° = 0 1) sin 45°+ cos 60° = 1/2( 2^1/2 + 1) 2) csc 45° tan 60° = 6^(1/2) 3) 4 sin 90° - 3 tan 180° = 4
Trig help: Find the exact value of the trig function at the given real number?
you have to use your special triangles - 45-45-90 and 30-60-90 find the reference angle for 2pi/3 that is the same as 120 degrees if that helps. the reference angle, then, is 60 Since you're in the second quadrant, the opp is positive root3 and the adj. is -1. The hyp is 2. so sin 2pi/3 = root3/2. cosine 2pi/3 is -1/2. tan 2pi/3 is root3/-1 = -root3