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具体回答如下：cos(π-x) = -cos x cos（π+x）= -cos x sin（π-x） = sinx sin（π+x）= sinx sinx 是在第1、2象限是正的，cosx 是1、4象限是正的。和角公式：sin ( α ± β ) = sinα · cosβ ± cosα · sinβsin ( α + β + γ ) = sinα · cosβ · cosγ + cosα · sinβ · cosγ + cosα · cosβ · sinγ - sinα · sinβ · sinγcos ( α ± β ) = cosα cosβ ∓ sinβ sinαtan ( α ± β ) = ( tanα ± tanβ ) ( 1 ∓ tanα tanβ ) Randy Novak@RandyNovak823 Related Topics:CommonCore (Functions)Common Corefor Mathematics Examples, solutions, videos, and lessons to help High School students learn how to use special triangles to determine geometrically the values of sine, cosine, tangent for π3, π4 and π6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number. Common Core: HSF-TF.A.3 The following diagram shows the unit circle for radians and degrees. Scroll down the page for more examples and solutions for trigonometric functions using the unit circle.Introduction to Trigonometric Functions Using TrianglesDefines trigonometric functions using right triangles.Show Step-by-step SolutionsSine, Cosine, and Tangent of π3, π4, π6This video demonstrates geometrically the values of Sine, Cosine, and Tangent for angles with radian measures π3, π4, π6.Show Step-by-step Solutions Trig Values of Special Angles F.TF.3Find the trigonometric function values at critical angles between 0 and π2, and use the unit circle to find trigonometric values at intervals of π (tangent) or 2π (sine and cosine) beyond them.Deriving Values on the Unit CircleDerive the values in the first quadrant of the unit circle using geometry and the pythagorean theorem.Show Step-by-step SolutionsA way to remember the Entire Unit Circle for TrigonometryShow Step-by-step Solutions Try the free Mathway calculator andproblem solver below to practice various math topics. Try the given examples, or type in your ownproblem and check your answer with the step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. Last updated at Dec. 6, 2018 by Teachoo sin (2π + x) = sin x cos (2π + x) = cos x tan (2π + x) = tan x Here x is an acute angle. and 2π = 2 × 180° = 360° Lets see why there are same. Suppose x = 390° x = 360° + 30° We note that x = 390° is the same as 30° So, we can write cos (390°) = cos (30°) sin (390°) = sin (30°) tan (390°) = tan (30°) Similarly, if the angle was x = 750° x = 2 × 360° + 30° Thus, we rotate twice and come back to 30° ∴ x = 750° is the same as 30° So, we can write cos (750°) = cos (30°) sin (750°) = sin (30°) tan (750°) = tan (30°) Thus, we observe that sin (n × 360° + x) = sin x where n = 1, 2, 3, 4, …. Writing in radians sin (n × 2π + x) = sin x cos (n × 2π + x) = cos x tan (n × 2π + x) = tan x where n = 1, 2, 3, 4, …. Note: For sec, cosec, cot … we convert them into sin, cos, tan and apply the sin, cos, tan formula Lets try some questions Find cos 390° First, we convert 390° into radians. We multiply by π180 x = 390 × π180 x = π × 390180 x = π × 136 x = 13π6 So, cos 390° = cos 13π6 Thus, cos 13π6 = cos (2π + π6) Since values of cos x repeats after an interval of 2π ,hence ignoring 2π = cos (π6) = cos (1806°) = cos 30° = √32 Find value of tan (–15 π 4) tan (–15π4) As tan (–x) = – tan x = – tan (15π4) = – tan (4π – π4) = – tan (–π4) As tan (–x) = – tan x = – (– tan (π4)) = tan (π4) = tan (1804 °) = tan (45°) = 1 ∴ tan (–15π4) = 1Support Teachoo in making more (and better content) - Monthly, 6 monthly, yearly packs available! guyun3456 1年前已收到1个回答举报赞 gebiao 幼苗共回答了17个问题采纳率：94.1% 举报化简：sinx+cosx=(1-√3)2.1sinx+cosx=(1-√3)2平方得：1+2sinxcosx=（4-2√3)4所以sinxcosx=√34.2由1、2得sinx=.cosx=.我只能算到这样了,自己算一下第二问无能为力 1年前 5 可能相似的问题已知sin x－cos x＝0,x∈（0,2／∏）求tan x及x的值 1年前1个回答已知sin²2α+sin2αcosα-cos2α=1α∈（0,π2）求sinα,tanα的值 1年前1个回答已知sin(x-135)cos(x-45)=-14,求cos4x 1年前1个回答已知sin（π-α）-cos（π+α）=23，（π2＜α＜π），求下列各式的值： 1年前1个回答【数学】已知sinα-(3π4)cosα-(π4)=-14,求cos4α的值. 1年前2个回答已知sinα＝13−cosα，则sin(π4−α)cos2α的值等于______． 1年前2个回答已知sin²2α+sin2αcosα-cos2α=1,α∈(0,π),求α. 1年前1个回答已知SINθ=45,COSθ=－35,则角2θ属于第几象限? 1年前1个回答已知sinα=-13,cosβ=23,且α β在同一象限,求sin（α-β）的值 1年前3个回答已知sinα=35,cos(α＋β)=513,且α,β均为锐角.1.求cosβ 2.比较α,β的大小 1年前5个回答已知sin角加cos角等于三分之根号二,求Tan 1年前2个回答已知sin(3π-α)=根号二cos(3π2+β),根号三cos（-α）=负根号二cos（π+β）,且0 1年前1个回答已知sin(x+π3)cos(x-π3)+cos(x-π3)sin(x-π3)=-(2根号23)且π 1年前1个回答已知sinα=23 cosβ= -34 α属于(π2,π) β是第三象限角,求cos(α+β),sin(α-β)的 1年前4个回答高一数学已知sin(π2-b)*cos(a+b)-sin(π+b)*sin(a+b)=35其中a∈(3π2,2π) 1年前1个回答已知sinα＝12+cosα，且α∈(0，π2)，则cos2αsin(α−π4)的值为（　　） 1年前2个回答已知sin²2α+sin2αcosα-cos2α=1,α∈(0,2π）,求sinα、tanα 1年前1个回答三角函数1.已知sina=513且a为第二象限角,求tana2.已知sin^4 a+cos^4 a=1,求sina+c 1年前2个回答已知sinα=k-1,cosα=4-3k,且α是第二象限角,则k的条件 1年前1个回答已知sin^2(x)+cos(x)+m=0有实数解,求m范围 1年前2个回答
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